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CHAMBERS’  EDUCATIONAL  COURSE. 


ELEMENTS 

OF 

NATURAL  PHILOSOPHY. 

3n  &l)rcc  parte. 

L 

LAWS  OF  MATTER  AND  MOTION. 


MECHANICS. 

hi. 

HYDROSTATICS,  HYDRAULICS,  AND  PNEUMATICS. 


WILLIAM  8c  ROBERT  CHAMBERS. 


EDITED  BY  D.  M.  REESE,  M.  D.,  LL.  D. 

NEW-YORK: 

PUBLISHED  BY  A.  S.  BARNES  k CO. 

PHILADELPHIA:  JOHN  BALL. 

H.  W.  DERBY  & CO. 

CINCINNATI. 

1849. 


CHAMBERS’  EDUCATIONAL  COURSE. 


The  object  of  the  following  works  is  to  furnish  the  friends  of  an  improved 
system  of  education  with  the  books  required  for  carrying  out  their  views,  in 
the  actual  business  of  the  school-room,  and  the  family  circle. 

The  Messrs.  Chambers  (whose  works  are  so  favorably  known  in  the  different 
departments  of  literature,  throughout  this  country  as  well  as  Europe)  have 
employed  the  first  professors  in  Scotland  in  the  preparation  of  these  works. 
They  are  now  offered  to  the  schools  of  the  United  States,  under  the  American 
revision  of  D.  M.  Reese,  M.  D.,  LL.  D.,  late  superintendent  of  public  schools 
of  the  city  and  county  of  New-York. 


I.— CHAMBERS’  TREASURY  OF  KNOWLEDGE.  (3 parts  in  one.) 

BY  W.  & R.  CHAMBERS. 

Part  1 Embraces  Elementary  Lessons  in  Common  Things  - or  things  which  lie  most  imme- 
diately around  us,  and  first  attract  the  attention  of  the  young  mind.  Part  2 Embraces 
Practical  Lessons  on  Common  Objects — such  as  articles  or  objects  from  the  Mineral.  Vege- 
table, and  Animal  Kingdoms,  manufactured  articles,  miscellaneous  substances  and  objects.  &c. 
Part  3 Embraces  Introduction  to  the  Sciences.  This  presents  a systematic  view  of  nature, 
under  the  various  sciences.  Care  is  taken  that  the  information  given  should  not  be  a 
superficial  view  of  a few  unconnected  phenomena,  but  a chain  of  principles  calculated,  in 
combination,  tf^npress  a distinct  and  comprehensive  idea  to  the  mind  of  the  very  young  child. 
This  volume  is  designed  for  an  early  reading  book,  that  the  scholar  may  be  exercised  in  reading, 
and  at  the  same  time  acquire  knowledge  of  such  subjects  as  bis  capacity  will  enable  him  to 
understand.  It  contains  much  useful  information  upon  common  objects  of  life. 

||. —CHAMBERS’  ELEMENTS  OF  DRAWING.  (2 parts  in  one.) 

BY  JOHN  CLARK. 

Part  1 Embraces  Exercises , for  the  Slate.  Part  2 Embraces  the  Principles  of  Drawing 
and  Perspective. 

With  but  very  few  exceptions,  children  are  fond  of  makiug  efforts  in  Drawing.  Furnished  with 
a black-lead  pencil  and  sheet  of  paper,  or  slate  and  pencil,  they  are  delighted  to  scribble 
whatever  their  fancy  suggests.  Followed  up  methodically  by  the  teacher,  their  infant 
aspirations  may  lead  to  the  development  of  much  valuable  talent.  Illustrated  by  Engravings. 

III.— CHAMBERS’  ELEMENTS  OF  NATURAL  PHILOSOPHY. 

THREE  PARTS  IN  ONE. 

Part  1 Embraces  Laws  of  Matter  and  Motion.  Part  2 Embraces  Mechanics.  Part  3 
Embraces  Hydrostatics , Hydraulics , and  Pneumatics. 

In  tha  treatment  of  the  several  subjects  great  care  has  been  taken  to  render  the  language  simple 
and  intelligible.  Illustrated  by  Wood  Engravings- 

IV.— CHAMBERS’  CHEMISTRY  AND  ELECTRICITY. 

(TWO  PARTS  IN  ONE.)  BY  D.  B.  REID  AND  ALEXANDER  BAIN. 

Part  1 Embraces  Illustrations,  and  experiments  of  the  Chemical  Phenomena  of  Daily  Life. 
By  D.  B.  Reid,  M.  D.,  F.  R.  S.  E.  Part  2 Embraces  Electricity , (statical  and  current.) 
By  Alexander  Bain,  the  original  inventor  of  Electric  and  Telegraphic  clocks. 

This  work  is  designed  to  facilitate  the  introduction  of  Chemistry  as  an  elementary  branch  of 
education  in  schools.  Illustrated  by  Engravings. 

V.— CHAMBERS’  VEGETABLE  AND  ANIMAL  PHYSIOLOGY. 

BY  G.  HAMILTON,  M.  D. 

Part  1 Embraces  the  General  Structure  and  Functions  of  Plants.  Part  2 Embraces  the 
Organization  of  Animals. 

The  object  of  this  work  is  to  unite  Vegetable  and  Animal  Physiology,  and  bring  both  systems 
under  one  head,  as  properly  connected  and  adapted  to  the  mind  of  tne  student. 

VI. — CHAMBERS’  ELEMENTS  OF  ZOOLOGY.  (Illustrated.) 

Presenting  a complete  view  of  the  Animal  Kingdom  as  a portion  of  external  nature.  As  the 

composition  of  one  of  the  most  eminent  physiologists  of  our  age,  it  possesses  an  authority  not 
attributable  to  such  treatises  in  general. 

VII. — CHAMBERS’  ELEMENTS  OF  GEOLOGY.  (Illustrated.) 

BY  DAVID  PAGE. 

The  subject  is  here  presented  in  its  two  aspects  of  interesting  and  important.  Interesting, 
inasmuch  as  it  exhibits  the  progressive  conditions  of  the  earth  from  the  remotest  periods,  and 
reveals  the  character  of  the  plants  and  animals  which  have  successively  adorned  and  peop  ed 
its  surface ; and  important,  as  it  determines  the  position  of  those  metals  and  minerals  upon 
which  the  arts  and  manufactures  so  intimately  depend. 


Entered  according  to  Act  of  Congress,  in  the  year  1S49,  by 
A.  S.  B ARNES' & CO.. 

in  the  Clerk’s  Office  of  the  District  Court  of  the  Southern  District  of  New-York. 


INTRODUCTORY  OBSERVATIONS 


BY  THE 

AMERICAN  EDITOR. 


The  present  volume  is  appropriately  styled  the  “First 
Book  of  Natural  Philosophy,”  because  its  subject  should  be 
understood  by  the  learner  before  entering  upon  the  study  of 
either  of  the  other  departments  of  Physics.  Moreover,  it  lies 
at  the  foundation  of  all  natural  science,  and  explains  a multi- 
tude of  the  phenomena  of  nature  and  art,  which  earliest 
awaken  the  curiosity  of  children  in  their  observation  of  natural 
objects,  and  in  their  various  forms  of  amusement.  The  lessons 
here  taught  will  enable  parents  or  teachers  to  satisfy  the  in- 
quisitiveness of  children,  who  often  manifest  an  ardent  thirst 
for  knowledge  in  the  nature  and  causes  of  things.  And  a 
thousand  opportunities  occur,  in  simple  and  familiar  occur- 
rences transpiring  in  connection  with  the  exercises  of  the 
school-room  and  the  pastimes  of  the  play-ground,  of  which 
teachers  and  scholars  may  avail  themselves  for  creating  a fond- 
ness for  this  beautiful  science. 

No  subject  so  forcibly  impresses  the  young  with  the  evi- 
dence of  a Supreme  Being,  or  so  strikingly  shows  the  proofs 
of  the  Divine  wisdom  and  goodness,  as  do  the  topics  of  this 
little  volume — presenting  thus  to  the  admiration  of  children 
the  grandest  truths  of  moral  science,  and  leading  them  to  sub- 
mit to  tbe  sublime  teachings  of  revelation. 

The  catechetical  questions  in  this,  as  in  the  other  volumes, 
are  so  framed  purposely  as  to  admit  of  other  and  kindred 
questions  on  almost  every  topic  which  will  readily  occur  to  the 
teacher;  while  to  the  illustrations  furnished  by  the  author, 
oilier  familiar  examples  may  be  superadded. 

That  this  work  may  inspire  teachers  and  pupils  with  a taste 
for  kindred  pursuits,  and  promote  their  intellectual  and  moral 
improvement,  is  the  confident  expectation  of  the  editor. 

D.  M.  R. 


PREFACE. 


The  Laws  of  Matter  and  Motion,  usually  treated  under  the 
titles  of  Statics,  Pyronomics  (or  Heat)  and  Dynamics,  form 
not  only  the  proper  introduction  to  Natural  Science,  but  that 
particular  department  of  it  with  which  it  is  of  the  most  im- 
portance that  all  should  be  made  familiar.  For  these  reasons, 
they  are  here  presented  in  a small  distinct  treatise,  the  price  if 
which,  as  well  as  the  simplicity  of  the  language  employed  in 
its  composition,  may  be  expected  to  facilitate  its  general  intro- 
duction into  schools  and  families. 

The  remaining  departments  of  Physics — Mechanics  or 
Mechanical  Powers  and  Machinery,  Hydrostatics  and  Hy- 
draulics, Pneumatics,  Acoustics,  and  Optics,  Electricity 
and  Magnetism,  Meteorology,  and  Astronomy,  constitute 
distinct  portions  of  this  Educational  Course,  already,  or 
about  to  be,  published. 

In  exercising  a class  in  this  and  other  departments  of  Natural 
Science,  it  will  be.  found  to  be  of  considerable  importance  to 
cause  each  paragraph  to  be  mastered  or  thoroughly  understood 
before  proceeding  to  what  follows ; for  the  whole  constitutes 
a structure  in  which  each  part  rests  on  what  has  gone  before 
it.  The  pupil  should,  also,  not  only  read,  but  be  induced  to 
think  on  the  nature  of  the  principles  which  are  unfolded,  and 
led  to  find  examples  of  their  action  in  the  every-day  concerns 
of  life,  and  the  common  phenomena  of  the  universe. 

To  facilitate  exercises,  and  afford  a ready  means  of  reference, 
each  paragraph  is  numbered.  [And  to  add  still  greater  facili- 
ties both  to  teachers  and  learners,  each  page  is  furnished  with 
analytical  questions.] 


CONTENTS. 


Page 

Of  Matter  and  its  Properties 7 

Impenetrability . 8 

Extension  or  Magnitude 9 

Figure 10 

Divisibility.. 10 

Inertia 13 

Attraction 17 

Capillary  Attraction 19 

Chemical  Attraction 20 

Magnetic  Attraction 22 

Electrical  Attraction  23 

Attraction  of  Gravitation 24 

The  Repulsive  Quality  in  Matter — Heat 29 

Repulsive  Quality  of  Heat 31 

Modifying  Quality  of  Heat 31 

Conduction  of  Heat 31 

Radiation  of  Heat. .. . 32 

Production  of  Heat, 32 

General  Distribution  of  Heat 33 

Temperature — The  Thermometer 33 

Repulsive  Energy — Boiling  Water 35 

Vaporific  Point — Steam 36 

Spontaneous  Evaporation 37 

Frost — Freezing  Point 38 

Equilibrium  of  Heat  and  Cold  39 

Artificial  Freezing  Apparatus 40 

Gradual  Alteration  of  Temperature 40  5 

Expansion  in  Cooling — Crystallization 41 

Point  of  greatest  Density  in  Water 41 

Effects  of  Frost 42 

Shrinking  of  Bodies  by  Heat 44 

Ignition  of  Bodies — Fire 44 

5 


7 


6 CONTENTS. 

Page 

Accidental  Properties  of  Matter 45 

Density  of  Bodies 45 

Porosity 49 

Compressibility 49 

Elasticity..... 50 

Dilatability 51 

Hardness 51 

Brittleness 51 

Malleability 51 

Ductility 52 

Tenacity 52 

Motion  and  Forces — General  Explanations 53 

The  Phenomena  of  Falling  Bodies — Weight 57 

The  Centre  of  Gravity 61 

The  Pendulum 69 

The  Laws  of  Motion 75 

Uniform  Motion  in  a Straight  Line 75 

Centrifugal  Force  and  Circular  Motion 77 

Laws  of  Projectiles 82 

Action  and  Reaction 85 

Motion  in  Elastic  Bodies 87 

Reflected  Motion 88 

Composition  of  Motion  and  Forces 90 

Common  Motion 94 


«■ 


NATURAL  PHILOSOPHY. 


MATTER  AND  MOTION. 


OF  MATTER  AND  ITS  PROPERTIES. 

1.  Matter  is  a term  applied  to  all  things  which  are 
supposed  to  possess  substance.  We  acquire  a knowledge 
that  things  possess  substance,  through  our  senses,  some- 
times aided  by  the  test  of  philosophical  experiment. 

2.  Matter  is  organic,  when  it  possesses  organs  or  organ- 
ized parts  for  sustaining  living  action.  Matter  is  inorganic, 
when  it  has  no  organs  or  organized  parts  to  sustain  living 
action.  Animals  and  plants  are  organic  matter ; a stone 
is  inorganic  matter. 

3.  Portions  of  matter  are  called  bodies.  The  air,  water, 
the  earth — a stone,  a ball,  an  animal,  a tree — any  substan- 
tial thing,  which  we  can  distinguish  from  other  things — 
are  bodies. 

4.  When  any  portion  of  matter  excites  any  of  our 
senses,  the  feeling  of  which  we  are  sensible  is  called  a 
sensation  ; and  our  knowledge  of  the  existence  of  the  ex- 
citing cause,  resulting  from  this  sensation,  is  called  a 
perception. 

5.  The  qualities  which  bodies  possess  of  exciting  par- 
ticular sensations,  are  called  their  properties. 

6.  The  phenomena  or  appearances  that  take  place  in 
the  material  world,  are  considered  to  be  the  result  of  cer- 


1.  What  is  matter,  and  how  is  it  recognised  ? 

2.  Define  organic  and  inorganic  matter. 

3.  Explain  bodies, — sensation,  perception,  properties,  &.c. 

7 


8 


IMPENETRABILITY. 


tain  natural  laws.  A natural  law  is  a rule,  or  principle, 
according  to  which  the  same  event  uniformly  occurs  under 
the  same  circumstances. 

7.  The  natural  laws  which  regulate  the  phenomena  of 
inorganic  matter  and  its  properties,  are  sometimes  called 
physical  laws,  from  a Greek  word  signifying  Nature  ; 
and  the  treatment  of  these  laws  is  ordinarily  expressed  by 
the  terms  Natural  Philosophy  or  Physical  Science. 

8.  The  constitution  of  a body  is  its  state  of  being,  or 
peculiar  composition  of  properties  and  qualities.  We 
cannot  alter  any  of  the  properties  or  qualities  of  a body, 
without  altering  the  constitution  of  the  body.  Bodies  have 
certain  properties,  which  are  called  essential,  because  they 
are  invariably  found  in  bodies.  The  essential  properties 
of  bodies  are  Impenetrability,  Extension,  Figure,  Divi- 
sibility, Inertia,  and  Attraction. 

IMPENETRABILITY. 

9.  By  impenetrability,  it  is  meant  that  two  bodies  can- 
not occupy  the  same  space  at  the  same  time.  Each  par- 
ticle of  matter  occupies  a certain  space,  and  the  same 
space  cannot  at  the  same  time  be  occupied  by  another 
particle.  What  common  language  calls  penetrability,  is, 
in  the  philosophical  sense,  only  a liability  to  have  certain 
particles  displaced.  Thus  a piece  of  dough  is,  in  common 
language,  penetrable  by  the  finger ; but  in  philosophical 
language,  the  act  of  thrusting  the  finger  into  a piece  of 
dough  would  be  called  the  displacing  of  as  much  of  the 
dough  as  the  space  occupied  by  the  finger.  Perhaps  the 
word  occupancy  would  be  a less  ambiguous  term  for  the 
philosophical  idea  of  impenetrability. 

10.  There  are  cases  in  which  a condensation  takes 
place,  when  two  fluids  are  mixed  together,  so  that  a con- 
siderable deal  less  space  is  occupied  by  the  two  together, 
than  was  occupied  by  them  in  a separate  state.  But  this 
arises  from  a chemical  combination  having  taken  place ; 
the  particles  of  the  substances,  by  the  mysterious  agency 

4.  What  of  the  constitution  of  a body  ? 

5 Enumerate  the  essential  properties  of  bodies. 

6.  Define  impenetrabilby,  and  illustrate. 


EXTENSION  OR  MAGNITUDE. 


9 


of  chemical  attraction,  have  been  drawn  closer  together; 
thus,  the  whole  fluid  occupies  less  space  than  it  did 
formerly.  In  the  same  way,  a sponge,  by  being  com- 
pressed, has  its  particles  brought  nearer  to  each  other,  and 
of  course  it  has  less  bulk  than  it  had  before  it  was 
squeezed.  Indeed,  the  hand  and  the  sponge  together 
may  occupy  the  same  space  as  the  sponge  did  singly. 

11.  A nail,  driven  into  a piece  of  wood  or  other  soft 
material,  under  certain  circumstances  does  not  enlarge  the 
general  size  of  the  body  ; but  in  penetrating  it,  it  displaces 
its  particles,  and  occupies  the  space  which  they  occu- 
pied ; and,  accordingly,  they  are  rendered  more  dense,  or 
become  more  solidified,  than  they  were  before,  just  in  the 
same  way  as  the  particles  of  the  sponge  when  compressed. 
In  the  one  case,  the  particles  are  condensed  from  without, 
and  in  the  other  from  within.  But  these  particles  still 
occupy  a certain  quantity  of  space  which  cannot  be  occu- 
pied by  other  particles  at  the  same  time,  for  in  every  case 
in  which  the  attempt  is  made,  although  this  apparently 
seems  to  be  effected,  it  will  be  found  that  the  one  has  been 
removed  to  make  way  for  the  other. 

EXTENSION  OR  MAGNITUDE. 

12.  All  bodies  which  are  observable  by  the  senses,  are 
lound  to  occupy  a certain  portion  of  space — that  is,  they 
possess  extension  or  magnitude ; and  those  which  are  so 
small  as  to  elude  investigation  in  this  manner,  are  con- 
sidered by  the  understanding  to  possess  it.  Indeed,  the 
impenetrability  of  matter  presupposes  its  extension  or 
magnitude.  It  is  impossible  to  form  a conception  of  matter, 
however  minute  may  be  the  particle,  without  connectmg 
with  it  the  idea  of  its  having  a certain  bulk,  and  filling  a 
certain  quantity  of  space. 

13.  In  common  phraseology,  we  express  this  property 
of  bodies  by  the  word  size  ; but  the  most  appropriate  term 
is  volume.  Thus,  we  say  the  volume  of  a terrestrial  or 
celestial  globe  is  so  many  cubic  inches.  When  the  lines 


1 Examples  of  condensation,  from  wi  hout  and  within, 

b.  What  of  nv  cast  n > 


10 


FIGURE DIVISI BIL1TY. 


and  surfaces  of  a body  are  spoken  of,  the  external  limits 
of  its  magnitude  are  implied.  Lines  are  the  limits  which 
separate  the  several  surfaces  of  the  same  body.  They  are 
also  called  edges.  Thus,  the  line  which  separates  the  top 
from  one  of  the  sides  of  a box,  is  denominated  an  edge. 
The  quantity  of  a surface. is  called  its  area,  and  the  quan- 
tity of  a line  is  termed  its  length.  Thus,  we  say  the  area 
of  a floor  is  so  many  yards  ; and  the  length  of  a rope  is 
so  many  yards.  Volume,  area,  and  length,  however,  are 
sometimes  expressed  by  the  word  magnitude. 

14.  The  dimensions  of  magnitude  or  extension  are 
usually  entitled  length,  breadth,  and  depth  ; and  they  vary 
of  course  very  considerably  in  different  bodies,  according 
to  their  shape.  Height  and  depth  are  the  same  dimen- 
sion, considered  in  different  points  of  view.  When  a body 
is  measured  downwards,  it  is  said  to  be  so  many  feet  deep ; 
when  measured  upwards,  it  is  said  to  be  so  many  feet 
high.  Breadth  and  width  express  the  same  dimension. 

FIGURE. 

15.  The  figure  of  a body  is  its  shape  or  form.  Figure 
or  form  is  the  result  of  extension,  for  we  cannot  have  the 
idea  of  a body  possessing  length  and  breadth,  without  its 
having  some  kind  of  figure,  however  irregular.  The 
volume  of  a body  has  no  relation  to  its  figure.  Bodies 
which  have  the  same  figure  may  possess  very  different 
volumes  ; and  bodies  may  have  the  same  volume,  but  pos- 
sess very  different  figures.  Thus,  two  masses  of  matter 
may  have  the  same  volume,  although  the  one  be  round 
and  the  other  be  square. 

DIVISIBILITY. 

16.  Matter  is  divisible  into  parts,  and  these  parts  may 
again  be  subdivided  into  other  parts.  By  this  is  meant 
divisibility  or  separability. 

17.  To  the  practical  subdivision  of  matter  there  seems 
to  be  no  assignable  limit ; and  many  of  the  instances  of  it 

9.  Define  volume,  area,  and  length,  &c. 

10.  What  of  figure  ? 

11.  Define  divisibility. 


DIVISIBILITY. 


11 


which  may  be  found  in  philosophical  investigations,  almost 
exceed  credibility.  The  thinnest  part  of  a soap  bubble, 
which  is  a thin  shell  of  water  and  the  matter  of  soap,  does 
not  exceed,  in  thickness,  the  2,500,000th  part  of  an  inch. 
The  useful  arts,  also,  furnish  many  striking  examples ; 
but  it  is  in  the  organized  world  that  the  most  astonishing 
proofs  of  the  extreme  divisibility  of  globules,  or  particles 
of  matter,  are  to  be  found. 

18.  Animalcules — that  is,  animals  which  are  so  small 
as  to  be  invisible  to  the  naked  eye,  and  which,  by  means 
of  microscopes,  are  seen  floating  in  water — are  in  some 
cases  so  minute,  that  it  would  require  a million  of  them  to 
form  the  bulk  of  a grain  of  sand.  As  these  animalcules 
possess,  in  every  case,  a perfect  organization  to  enable 
them  to  perform  all  the  functions  of  life,  the  smallness  of 
their  different  parts,  and  the  extreme  minuteness  of  the 
particles  of  matter  which  compose  them,  are  too  exquisite 
to  be  made  the  subject  of  calculation  : the  imagination  is 
lost  in  the  contemplation  of  their  wonderful  economy. 

19.  The  effluvium  or  odour  which  excites  the  sensation 
of  sm?//,  consists  of  an  incalculable  number  of  particles  of 
matter  floating  in  the  atmosphere,  and  so  minute  as  to  be 
altogether  invisible  to  the  eye.  These  particles  are  not 
more  remarkable  for  their  inconceivably  small  size  than 
for  the  length  of  time  which  they  will  remain  in  suspen- 
sion in  the  atmosphere,  or  in  connection  with  some  par- 
ticular place.  The  effluvium  given  forth  by  a single  grain 
of  musk  has  been  known  to  perfume  a large  apartment  for 
twenty  years,  and  yet  at  the  expiry  of  that  period  there 
was  no  sensible  diminution  of  the  little  mass  of  matter  from 
which  the  smell  had  proceeded. 

20.  The  diffusion  of  particles  of  matter  invisible  to  the 
naked  eye,  is  also  obvious  in  the  case  of  the  melting  of  a 
piece  of  sugar  in  our  tea  : the  solid  mass  of  the  sugar  dis- 
appears, and  the  particles  of  which  it  was  composed  are 
diffused  in  the  liquid.  There  is  a similar  diffusion  of  par- 
ticles of  salt  in  the  ocean.  When  we  look  through  a glass 


12.  What  example  of  divisibility  is  named? 

13.  What  of  animalcules,  and  of  odours  ? 


12 


DIVISIBILITY. 


full  of  sea  water,  we  perceive  that  it  is  pure  and  limpid ; 
but  if  we  pour  the  water  into  a vessel  on  the  fire,  and  boil 
it,  we  shall  at  length  discover  that,  while  the  liquid  has 
escaped  in  the  form  of  vapour,  the  particles  of  salt  it  held 
in  solution  remain  encrusted  on  the  vessel. 

21.  Particles  of  matter  are  never  destroyed  or  lost, 
although  they  may  disappear  from  our  immediate  obser- 
vation. Under  certain  circumstances,  the  particles  may 
again  be  collected  into  a body  without  change  or  form. 
Mercury,  water,  and  many  other  substances,  may  be  con- 
verted into  vapour,  or  distilled  in  close  vessels,  without 
any  of  their  particles  being  lost.  In  such  cases,  there  is 
no  decomposition  of  the  substances,  but  only  a change  of 
form  by  the  heat ; and  hence  the  mercury  and  water 
assume  their  original  state  again  on  cooling. 

22.  When  bodies  suffer  decomposition  or  decay,  their 
elementary  particles,  in  like  manner,  are  neither  destroyed 
nor  lost,  but  only  enter  into  new  arrangements,  or  combi- 
nations with  other  bodies.  When  a piece  of  wood  is 
heated  in  a close  vessel,  such  as  a retort,  we  obtain  water, 
an  acid,  several  kinds  of  gas,  and  there  remains  a black, 
porous  substance,  called  charcoal.  The  wood  is  thus  de- 
composed, or  destroyed, and  its  particles  take  a new  arrange- 
ment, and  assume  new  forms  ; but  that  nothing  is  lost,  is 
proved  by  the  fact,  that  if  the  water,  acid,  gases,  and  char- 
coal, be  collected  and  weighed,  they  will  be  found  exactly 
as  heavy  as  the  wood  was,  before  distillation.  In  the  same 
manner,  the  substance  of  the  coal  burnt  in  our  fires  is  not 
annihilated  ; it  is  only  dispersed  in  the  form  of  smoke,  or 
particles  of  culm,  gas,  and  ashes  or  dust.  Bones,  flesh,  or 
any  animal  substance,  may  in  the  same  manner  be  made 
to  assume  new  forms,  without  losing  a particle  of  the 
matter  which  they  originally  contained.  The  decay  of 
animal  or  vegetable  bodies  in  the  open  air,  or  in  the 
ground,  is  only  a process  by  which  the  particles  of  which 


14.  The  example  of  solution. 

15.  How  do  you  prove  that  nothing  is  lost  by  vaporization  ? 

16.  What  becomes  of  the  elements  after  decomposition  1 

17.  In  the  case  of  wood,  how  is  this  shown  ? 


INERTIA  OF  MATTER. 


13 


they  were  composed  change  their  places,  and  assume  new 
forms. 

23.  The  decay  and  decomposition  of  animals  and  vege- 
tables beneath  the  surface  of  the  earth,  fertilize  the  soil, 
which  nourishes  the  growth  of  plants  and  other  vegetables  ; 
and  these,  in  their  turn,  form  the  nutriment  of  animals. 
Thus  is  there  a perpetual  change  from  death  to  life,  and 
from  life  to  death,  and  as  constant  a succession  in  the  forms 
and  places  which  the  particles  of  matter  assume.  Nothing 
is  lost,  and  not  a particle  of  matter  is  struck  out  of  exist- 
ence. The  same  matter  of  which  every  living  animal  and 
every  vegetable  was  formed  in  the  earliest  ages,  is  still  in 
existence.  As  nothing  is  lost  or  annihilated,  so  it  is  pro- 
bable that  nothing  has  been  added,  and  that  we  ourselves 
are  composed  of  particles  of  matter  as  old  as  the  creation. 
In  time,  we  must  in  our  turn  suffer  decomposition,  as  all 
forms  have  done  before  us,  and  thus  resign  the  matter  of 
which  we  are  composed,  to  form  new  existences. 

24.  Such  are  some  of  the  remarkable  phenomena  con- 
nected with  the  divisibility  of  matter ; and  we  are  naturally 
led  to  inquire,  Is  matter  infinitely  divisible,  or  are  there 
certain  constituent  atoms  which  are  incapable  of  furthei 
division  ? The  latter  supposition  is  the  one  most  generally 
admitted,  yet  there  is  no  denying  that  it  seems  scarcely  a 
legitimate  inference.  For  however  small  a particle  may 
be,  we  can  easily  conceive  of  one  still  smaller — for  instance, 
by  simply  supposing  that  same  particle  halved.  To  the 
understanding,  without  reference  to  direct  observation,  it 
seems  as  absurd  to  assign  limits  to  the  divisibility  of  matter, 
as  boundaries  to  space,  which  is  considered  infinite. 

INERTIA. 

25.  Inertia  means  passiveness  or  inactivity.  Thus, 
matter  is  perfectly  passive  in  submitting  to  any  condition 
in  which  it  is  placed,  whether  of  rest  or  motion.  When 
at  rest,  it  shows  an  inability  or  reluctancy  to  move  ; and 


18.  What  of  the  reciprocal  interchange  between  life  and  death  ? 
18.  What  reflections  are  suggested  ? 

20.  Define  inertia,  both  in  rest  and  motion. 


n 


INERTIA  OF  MATTER. 


when  in  motion,  it  show's  an  equal  inability  or  reJuctancy 
to  come  to  a state  of  rest. 

2(5.  It  is  obvious  that  a rock  on  the  surface  of  the  earth 
never  changes  its  position  in  respect  to  other  things  on  the 
earth.  It  has  of  itself  no  power  to  move,  and  w'ould  there- 
fore for  ever  lie  still,  unless  moved  by  some  external  force. 
Now,  it  is  just  as  true  that  inert  matter  has  no  pow'er  to 
bring  itself  to  rest,  when  once  put  in  motion,  as  that  it 
cannot  put  itself  in  motion,  when  at  rest ; for,  having  no 
life,  it  is  perfectly  passive,  both  to  motion  and  rest,  and 
therefore  either  state  depends  entirely  upon  external  cir- 
cumstances. 

27.  Many  instances  might  be  given  of  the  tendency 
which  matter  has  to  remain  in  the  condition  in  w'hich  it 
happens  to  have  been  already  placed.  The  following  are 
among  the  most  instructive  : — When  the  sails  of  a ship 
are  loosened  to  the  breeze,  slowly  and  heavily  at  first  the 
vessel  gets  into  motion,  but  gradually  its  speed  increases 
as  the  force  by  which  it  is  impelled  overcomes  the  inertia 
of  its  mass.  A great  force  is  necessary  at  first  to  set  a 
vehicle  in  motion  ; but  when  once  this  is  effected,  it  goes 
omvard  with  comparative  ease,  so  that,  in  fact,  a strong 
effort  is  necessary  before  it  can  be  stopped,  if  a person 
be  standing  in  it  when  it  is  suddenly  set  a-going,  his  feet 
are  pulled  forward,  whilst  his  body,  obeying  the  law'  of 
inertia,  remains  where  it  wras,  and  he  accordingly  falls 
backwards.  On  the  other  hand,  if  the  vehicle  be  suddenly 
stopped,  and  the  individual  be  standing  in  the  same  posi- 
tion as  formerly,  the  tendency  w'hich  his  body  has  to  move 
forwmrd — for  it  acquired  the  same  motion  as  the  carriage 
by  which  it  was  borne  along — will  cause  him  to  fall  in  the 
opposite  direction.  Casualties  of  this  description  fre- 
quently occur  to  persons  on  horseback,  who  are  thrown 
over  the  necks  of  their  steeds,  or  fall  behind  them,  accord- 
ing as  the  animal  stands  still  suddenly,  or  starts  off  unex- 
pectedly. A man  jumping  from  a coach  at  full  speed  will 
certainly  fall  prostrate  on  the  ground,  if  he  leaps  down  as 

21.  What  illustrations  are  cited  i 

22.  To  what  casualties  does  this  render  us  liable  f 

23.  What  of  jumping  from  a coach  in  motion  ? 


EXAMPLES  OF  INERTIA. 


15 


if  he  were  descending  from  a body  at  rest,  to  one  which  is 
in  the  same  state  ; for  when  he  makes  the  attempt,  his 
body  has  the  same  motion  as  the  coach  ; and  when  the 
feet  arrive  at  the  ground,  the  motion  in  the  lower  part  is 
arrested,  whilst  it  continues  in  the  upper  part ; and  thus 
he  finds  himself  thrown  from  the  perpendicular  into  the 
horizontal  position. 

28.  The  following  is  a familiar  example  of  the  inertia 
of  matter : — upon  the  tip  of  the  finger  let  a card  be  balanced, 
and  a piece  of  money — say  a shilling — laid  upon  it.  Let 
the  card  then  be  smartly  struck,  and  it  will  fly  from  be- 
neath the  coin,  leaving  it  supported  upon  the  finger. 
This  arises  from  the  inertia  of  the  metal  being  greater 
than  the  friction  of  the  card  which  passes  from  beneath  it. 

29.  Coursing,  or  hare-hunting,  affords  a striking  illus- 
tration of  inertia.  In  that  field  sport,  the  hare  seems  to 
possess  an  instinctive  consciousness  of  the  existence  of  this 
law  of  matter.  When  pursued  by  the  greyhound,  it  does 
not  run  in  a straight  line  to  the  cover,  but  in  a zig-zag  one. 
It  doubles,  that  is,  suddenly  changes  the  direction  of  its 
course,  and  turns  back  at  an  acute  angle  with  the  direction 
in  which  it  had  been  running.  The  greyhound,  being 
unprepared  to  make  the  turn,  and  therefore  unable  to 
resist  the  tendency  to  persevere  in  the  rapid  motion  which 
it  has  acquired,  is  impelled  a considerable  distance  forward 
before  it  can  check  its  speed  and  return  to  the  pursuit. 
But,  in  the  mean  time,  the  hare  has  been  enabled  to  shoot 
far  ahead  in  the  other  direction  ; and  although  a hare  is 
much  less  fleet  than  a greyhound,  by  this  scientific  ma- 
noeuvring it  often  escapes  its  pursuer.  Those  who  have 
witnessed  horse-racing,  may  have  observed  that  the  horses 
shoot  far  past  the  winning-post  before  their  speed  can 
be  arrested.  This  is  also  owing  to  the  inertia  of  their 
bodies. 

30.  Common  experience  proving  that  matter  does  not 
put  itself  in  motion,  we  might  be  led  to  believe  that  rest  is 
the  natural  state  of  all  inert  bodies  ; but  a few  consider- 


24.  What  example  is  named  ? 

25.  What  of  racing  and  hare-hunting  ? 


IB 


EXAMPLES  OF  INERTIA. 


ations  will  show  that  motion  is  as  much  the  natural  state  of 
matter  as  rest,  and  that  either  state  depends  on  the  resist- 
ance, or  impulse,  of  external  causes. 

31.  If  a cannon-ball  be  rolled  upon  the  ground,  it  will 
soon  cease  to  move,  because  the  ground  is  rough,  and 
presents  impediments  to  its  motion ; hut  if  it  be  rolled  on 
the  ice,  its  motion  will  continue  much  longer,  because 
there  are  fewer  impediments,  and,  consequently,  the  same 
force  of  impulse  will  carry  it  much  farther.  We  see  from 
this,  that,  with  the  same  impulse,  the  distance  to  which 
the  ball  will  move  must  depend  on  the  impediments  it 
meets  with,  or  the  resistance  it  has  to  overcome.  But 
suppose  that  the  ball  and  ice  were  both  so  smooth  as  to 
remove  as  much  as  possible  the  resistance  caused  by  fric- 
tion, then  it  is  obvious  that  the  ball  would  continue  to  move 
longer,  and  go  to  a greater  distance.  Next,  suppose  we 
avoid  the  friction  of  the  ice,  and  throw  the  ball  through 
the  air,  it  would  then  continue  in  motion  still  longer  with 
the  same  force  of  projection,  because  the  air  alone  presents 
less  impediment  than  the  air  and  ice,  and  there  is  now 
nothing  to  oppose  its  constant  motion,  except  the  resist- 
ance of  the  air. 

32.  If  the  air  be  exhausted  or  pumped  out  of  a vessel 
by  means  of  an  air-pump,  and  a common  top,  with  a small 
hard  point,  be  set  in  motion  in  it,  the  top  will  continue  to 
spin  a considerable  length  of  time,  because  the  air  does 
not  resist  its  motion.  A pendulum,  set  in  motion  in  an 
exhausted  vessel,  will  continue  to  swing,  without  the  help 
of  clockwork,  for  a whole  day,  because  there  is  nothing  to 
resist  its  perpetual  motion  but  the  small  friction  at  the  point 
where  it  is  suspended. 

33.  We  see,  then,  that  it  is  the  resistance  of  the  air, 
and  of  friction,  and  of  gravitation,  which  causes  bodies  once 
in  motion  to  cease  moving,  or  come  to  rest ; and  that  dead 
matter,  of  itself,  is  equally  incapable  of  causing  its  own 
motion,  or  its  own  rest. 

26.  Describe  ihe  motion  of  a ball  upon  the  ground  end  upon  the  ice. 

27.  How  is  motion  affected  by  excluding  the  air  t 

28.  What  agencies  combine  to  bring  bodies  to  rest  ? 


ATTRACTION. 


17 


THE  PROPERTIES  OF  MATTER  CONTINUED. 

ATTRACTION. 

34.  It  is  a fundamental  law  of  nature,  ascertained  by  Sir 
Isaac  Newton,  that  every  atom  or  particle  of  matter  has  a 
tendency  to  approach  or  to  be  attracted  towards  another 
atom  or  particle.  This  forms  one  of  the  leading  principles 
in  modern  natural  philosophy.  Experience  and  observa- 
tion demonstrate  that  this  power  of  mutual  attraction  per- 
vades all  material  things,  and,  though  unseen  except  in 
its  results,  is  ever  present  with  us  ; is  the  cause  of  particles 
of  matter  adhering  to  each  other,  and  forming  solid  masses 
— of  these  masses  assuming  in  many  instances  a round  or 
globular  form — of  the  falling  of  bodies  to,  and  their  stabi- 
lity on,  the  earth — and  is  one  of  the  causes  of  the  whole 
of  the  planetary  bodies  moving  in  their  paths  in  the 
heavens. 

35.  Attraction  is  of  different  kinds,  although  some  of 
these  may  be  merely  modifications  of  others,  and  has  re- 
ceived different  names  according  to  the  circumstances  under 
which  it  acts.  The  force  which  keeps  the  particles  of 
matter  together,  to  form  bodies,  or  masses,  is  called  attrac- 
tion of  cohesion.  That  which  inclines  different  masses 
towards  each  other,  is  called  gravitation , or  attraction  <f 
gravitation.  That  which  causes  liquids  to  rise  in  tubes, 
or  in  very  confined  situations,  is  called  capillary  attraction. 
That  which  forces  the  particles  of  different  kinds  to  unite, 
is  called  chemical  attraction.  That  which  causes  the  mag- 
netic needle  to  point  constantly  towards  the  poles  of  the 
earth,  is  magnetic  attraction.  And  that  which  is  excited 
by  friction  in  certain  substances,  is  known  by  the  name  of 
electrical  attraction. 

36.  Attraction  of  cohesion  acts  only  at  insensible  dis- 
tances, as  when  the  particles  of  bodies  apparently  touch 
each  other. 


29.  What  of  attraction,  and  how  manifested  ? 

30.  How  many,  and  what  kinds  of  attraction  are  named? 

31.  How  does  cohesion  act,  and  in  what  forms  of  bodies  ? 


18 


ATTRACTION  OF  COHESION. 


37.  This  kind  of  attraction  may  be  described  as  the 
quality  in  nature  which  causes  matter  to  cohere  or  stick 
together.  It  is  much  stronger  in  some  bodies  than  in 
others.  It  is  stronger  in  the  metals  than  in  most  other 
substances,  and  in  some  of  the  metals  it  is  stronger  than 
in  others.  In  general,  it  is  most  powerful  among  the 
particles  of  solid  bodies,  weaker  among  those  of  fluids, 
and  least  of  all,  or  almost  entirely  wanting,  among  elastic 
fluids,  such  as  air  and  the  gases. 

38.  Thus,  a small  iron  wire  will  hold  a suspended 
weight  of  many  pounds,  without  having  its  particles  sepa- 
rated ; the  particles  of  water  are  divided  by  a very  small 
force,  while  those  of  air  are  still  more  easily  moved  among 
each  other.  These  different  properties  depend  on  the 
force  of  cohesion  wdth  which  the  several  particles  of  these 
bodies  are  united. 

39.  When  the  particles  of  a body  can  be  suspended  in 
the  air  in  a fluid  state,  they  will,  if  not  under  the  attractive 
influence  of  some  other  body,  arrange  themselves  by  virtue 
of  the  same  law,  around  a centre,  and  take  a spherical  or 
round  form.  Thus,  a small  quantity  of  dew  suspended  on 
the  point  of  a thorn  or  leaf,  becomes  a globule,  because  in 
that  case  the  attraction  of  the  particles  towards  their  own 
centre  is  greater  than  the  attraction  of  any  neighbouring 
body.  Tears  running  down  the  cheeks,  drops  of  rain, 
and  hail,  are  all  examples  of  this  tendency  in  insulated 
fluid  bodies  to  assume  the  globular  form.  When  two 
perfect  globules  of  mercury  are  brought  into  contact,  they 
instantly  unite  together,  and  form  one  spherical  drop. 
The  manufacture  of  shot  is  also  a striking  illustration. 
The  lead  is  melted  and  poured  into  a sieve,  at  the  height 
of  about  two  hundred  feet  from  the  ground.  Each  stream 
of  lead,  immediately  after  leaving  the  sieve,  separates  into 
little  globules,  which,  before  they  reach  the  ground,  are 
cooled  and  become  solid  : thus  is  formed  the  shot  used  by 
sportsmen.  To  account  for  the  globular  form  in  all  these 


32.  How  is  the  difference  illustrated  ? 

33.  What  of  the  globular  or  spherical  form  ? 

34.  How  is  this  shown  in  shot-  towers  f 


CAPILLARY  ATTRACTION. 


19 


cases,  we  have  only  to  consider  that  the  particles  of  matter 
are  mutually  attracted  towards  a common  centre,  and  in 
liquids,  being  free  to  move,  they  arrange  themselves  ac- 
cordingly. 

49.  In  consequence  of  this  law  of  nature,  it  is  considered 
probable  that  the  planetary  bodies,  including  our  earth, 
were  originally  in  a fluid  state — that,  in  that  state,  they 
unavoidably  assumed  a spherical  form,  and  were  then 
hardened  into  their  present  consistency. 

CAPILLARY  ATTRACTION. 

41.  The  force  by  which  small  tubes,  or  porous  sub- 
stances, raise  liquids  above  their  levels,  is  called  Capillary 
Attraction,  from  capi/la,  the  Latin  word  for  a hair. 

42.  In  a wet  tea-cup,  or  other  vessel  containing  liquid, 
you  may  perceive  the  liquid  at  the  sides  rising  above  the 
level  of  that  of  the  other  parts  of  the  surface ; this  is 
caused  by  attraction. 

43.  If  two  glass  plates  be  brought  very  near  each  other, 
so  as  to  stand  parallel  with  their  flat  sides  in  almost  mutual 
contact,  and  then  their  lower  end  be  dipped  into  a vessel 
of  water,  the  fluid  will  rise  up  between  the  plates,  and  the 
height  to  which  it  rises  will  be  greater  the  nearer  the 
plates  are  to  each  other.  The  water  rises  very  little  on 
the  outsides  of  the  plates,  for  this  attraction  is  insensible 
at  even  moderately  small  distances.  If  a glass  tube,  with 
an  exceedingly  small  or  capillary  bore,  be  dipped  in  water, 
the  fluid  will  rise  in  the  interior  of  the  tube;  and  the 
smaller  the  bore,  the  higher  does  the  water  ascend. 

44.  A great  variety  of  porous  substances  are  capable 
of  this  kind  of  attraction.  If  a piece  of  sponge  or  a lump 
of  sugar  be  placed,  so  that  its  lowest  corner  touches  the 
water,  the  fluid  will  rise  up  and  wet  the  whole  mass.  In 
the  same  manner,  the  wick  of  a lamp  will  carry  up  the  oil 
to  supply  the  flame,  though  the  flame  is  several  inches 


35.  What  inference  is  thence  drawn  of  the  original  state  of  the 
earth  and  other  planets. 

36.  Define  capillary  attraction  and  give  an  instance. 

37.  What  other  illustrations  are  cited  ? 


20 


CHEMICAL  ATTRACTION. 


above  the  level  of  the  oil.  If  the  end  of  a towel  happens 
to  be  left  in  a basin  of  water,  it  will  empty  the  basin  of  its 
contents  ; and,  on  the  same  principle,  when  a dry  wedge 
of  wood  is  driven  into  the  crevice  of  a rock,  and  after- 
wards moistened  with  water,  as  when  the  rain  falls  upon 
it,  it  will  absorb  the  water,  swell,  and  sometimes  split 
the  rock. 

45.  It  is  this  kind  of  attraction  which  is  supposed  to  be 
one  of  the  causes  of  springs  of  water  in  the  earth.  The 
water  creeps  up  by  capillary  attraction  through  porous 
beds  of  sand,  small  stones,  and  crevices  of  rocks,  and  in 
this  manner  reaches  the  surface  even  at  great  heights. 
The  lower  parts  of  the  walls,  and  also  the  earthen  floors 
of  cottages,  are  in  the  same  manner  apt  to  become  damp, 
by  the  attraction  of  the  moisture  upwards  from  the  ground. 
Hence  the  necessity  for  clearing  away  all  wet  earthy 
matter  from  the  foundations  of  houses. 

CHEMICAL  ATTRACTION. 

46.  The  material  world  immediately  under  our  obser- 
vation, including  such  parts  of  the  earth’s  crust  as  have 
been  explored,  the  plants  and  animals  upon  the  earth, 
and  the  atmosphere  which  envelopes  it,  is  found  to  consist 
of  fifty -four  substances,  just  as  all  the  words  which,  com- 
pose a language  are  resolvable  into  a few  letters.  These 
substances,  having  hitherto  resisted  all  endeavours  to 
divide  or  resolve  them  into  any  others,  are  termed  the 
elements  of  matter , or  simple  bodies.  From  the  earliest 
stage  of  creation,  most  of  them  appear  to  have  been  in  a 
state  of  combination  with  each  other ; they  are  scarcely 
ever  naturally  found  otherwise  ; creation  itself  appears  to 
have  consisted  in  putting  them  into  the  associations  which 
they  have  since  commonly  displayed. 

47.  Matter  has  ever  been,  and  is  now,  undergoing  per- 
petual decompositions  and  recombinations  ; some  of  which 
take  place  upon  an  extensive  scale,  as  part  of  the  regular 
functions  and  operations  of  nature,  while  others  are  affected 


3V.  Between  what  portions  of  matter  is  chemical  a'traciion  exerted  ! 
3y.  How  many  elements  compose  the  universe  ? 


CHEMICAL  ATTRACTION. 


21 


by  the  ingenuity  of  man,  to  serve  the  purposes  of  his 
ordinary  economy.  Of  the  fifty-four  simple  substances, 
six  are  gases,  forty-two  are  metals,  and  the  remaining 
bodies  are  reducible  under  no  fixed  class.  The  investiga- 
tion of  the  laws  under  which  these  various  elementary 
bodies  have  formed  the  numerous  compound  substances 
which  we  see  in  nature,  and  the  means  by  which  com- 
pound substances  can.  be  resolved  into  their  original  ele- 
ments, or  thrown  into  new  combinations,  are  the  objects 
of  the  Science  of  Chemistry. 

48.  Chemical  attraction,  which  is  one  of  the  leading 
principles  in  chemistry,  takes  place  when  particles  of  dif- 
f rent  kinds  of  matter  unite,  and  the  particles  thus  formed 
have  properties  in  which  they  differ  more  or  less  from 
those  substances  by  whose  union  they  were  formed.  This 
species  of  attraction  is  also  known  under  the  name  of 
chemical  affbriti/,  because  it  is  said  that  the  particles  of 
substances,  having  an  affinity  for  each  other,  will  unite, 
while  those  having  no  affinity,  do  not  readily  enter  into 
union. 

4 ti.  It  might  almost  be  supposed  that  there  are  such 
things  as  preferences  and  dislikes  among  the  particles  of 
matter.  Thus,  if  a piece  of  marble  be  thrown  into  sul- 
phuric acid,  their  particles  will  unite  with  great  rapidity 
and  commotion,  and  there  will  result  a compound  differing 
in  all  respects  from  the  acid  or  the  marble.  But  if  a piece 
of  glass,  quartz,  gold,  or  silver,  be  thrown  into  the  acid,  no 
change  is  produced  on  either,  because  their  particles  have 
no  affinity. 

50.  Shake  sand  and  water  in  a bottle ; whenever  the 
agitation  ceases,  the  sand  falls  ; the  water  has  no  chemical 
action  with  it. 

51.  Suspend  a piece  of  aqueous  sulphate  of  copper 
(common  blue  vitriol)  with  a thread  in  a glass  full  of 
water.  The  particles  of  both  combine,  and  form  a stream 

* See  Reid’s  Rudiments  of  Chemistry,  forming  parts  of  Cham- 
bers’s Educational  Course. 


40.  Describe  these  in  classes. 

41.  What  of  chemical  affinity,  illustrate  this  ? 


22 


MAGNETIC  ATTRACTION. 


of  blue  fluid,  which  descends  from  the  points  where  they 
are  in  contact.  The  solid  is  said  to  be  dissolved.  The 
compound  is  called  a solution  of  the  solid. 

52.  Sulphur  and  quicksilver,  when  heated  together, 
will  form  a beautiful  red  compound,  known  under  the 
name  of  vermilion , and  which  has  none  of  the  qualities 
of  sulphur  or  quicksilver. 

5:5.  Oil  and  water  have  no  affinity  for  each  other,  but 
potash  has  an  attraction  for  both ; and  therefore  oil  and 
water  will  unite  when  potash  is  mixed  with  them.  In 
this  manner,  the  well-known  article  called  soap  is  formed. 
But  the  potash  has  a stronger  attraction  for  an  acid  than 
it  has  for  either  the  oil  or  the  water ; and,  therefore,  when 
soap  is  mixed  with  an  acid,  the  potash  leaves  the  oil,  and 
unites  with  the  acid  ; thus  destroying  the  old  compound, 
and  at  the  same  instant  forming  a new  one.  The  same 
happens  when  soap  is  dissolved  in  any  water  containing 
an  acid,  as  the  water  of  the  sea,  and  of  certain  wells. 
The  potash  forsakes  the  oil,  and  unites  with  the  acid, 
thus  leaving  the  oil  to  rise  to  the  surface  of  the  water. 
Such  waters  are  called  hard , and  are  not  good  for  wash- 
ing, on  account  of  the  floating  oil. 

MAGNETIC  ATTRACTION. 

54.  There  is  a certain  ore  of  iron,  a piece  of  which, 
being  suspended  by  a thread,  will  always  turn  one  of  its 
sides  to  the  north.  This  is  called  the  Loadstone,  or 
natural  Magnet ; and  when  it  is  brought  near  a piece  of 
iron,  or  steel,  a mutual  attraction  takes  place,  and,  under 
certain  circumstances,  the  two  bodies  will  come  together, 
and  adhere  to  each  other.  This  is  called  Magnetic  At- 
traction. When  a piece  of  steel  or  iron  is  rubbed  with  a 
magnet,  the  same  virtue  is  communicated  to  the  steel,  and 
it  will  attract  other  pieces  of  steel,  and  if  suspended  by  a 
string,  one  of  its  ends  will  constantly  point  towards  the 
north,  while  the  other,  of  course,  points  towards  the  south. 
This  is  called  an  artificial  magnet.  The  magnet  ic  needle 


42.  What  experiments  are  here  cited  ? 

43.  Detine  magnetic  attraction,  and  its  uses. 


ELECTRICAL  ATTRACTION. 


23 


is  a piece  of  steel,  first  touched  with  the  loadstone,  and 
then  suspended  so  as  to  turn  easily  on  a point.  By 
means  of  this  instrument,  which  is  called  the  Mariner’s 
Compass,  the  sailor  is  enabled  to  guide  his  ship  through 
the  pathless  ocean. 

ELECTRICAL  ATTRACTION. 

55.  All  nature  appears  to  be  pervaded  by  a mysterious 
affection,  which  bears  the  name  of  Electricity,  in  con- 
sequence of  its  having  been  supposed  by  the  ancients  to 
reside  exclusively  in  electron,  or  amber. 

56.  In  its  ordinary  state,  electricity  is  invisible  ; but 
when  excited,  it  assumes  the  appearance  of  a bright  and 
subtile  fluid.  It  is  sometimes  excited  in  very  tremendous 
forms  in  the  atmosphere  ; but  it  can  be  produced  in  less 
extent  by  mechanical  means,  particularly  by  the  rubbing 
of  amber,  glass,  silk,  and  a few  other  bodies. 

57.  When  a piece  of  glass,  or  sealing-wax,  is  rubbed 
with  the  dry  hand,  or  a piece  of  cloth,  and  then  held  to- 
wards any  light  substance,  such  as  hair,  or  thread,  the 
light  body  will  be  attracted  by  it,  and  will  adhere  for  a 
moment  to  the  glass  or  wax.  The  influence  which  thus 
moves  the  light  body  is  called  Electrical  Attraction. 
When  the  light  body  has  adhered  to  the  surface  of  the 
glass  for  a moment,  it  is  again  thrown  off,  or  repelled,  and 
this  is  called  Electrical  Repulsion. 

58.  It  is  the  nature  of  electricity  to  remain  in  a state 
of  equilibrium  or  balance  in  all  substances  ; and  when 
one  body  happens  to  have  more  than  its  natural  propor- 
tion, while  another  has  less,  there  is  a tendency  in  the  sur- 
plus, in  the  one  body,  if  sufficiently  near,  to  rush  to  make 
up  the  deficiency  in  the  other. 

59.  Electricity  is  the  cause  of  the  phenomena  of  thun- 
der and  lightning.  In  particular  states  of  the  atmo- 
sphere, generally  in  hot  weather,  the  balance  of  electricity 
among  the  clouds,  or  between  the  atmosphere  and  the 
earth,  is  apt  to  become  disturbed.  If  a cloud  containing 

44.  What  of  electricif,  and  i's  sources? 

45.  What  of  electrical  attraction  and  repulsion  ? 

46.  How  is  an  equilibrium  produced  ? 

47.  What  of  lightning  and  thunder  ? 


24 


ATTRACTION  OF  GRAVITATION. 


an  overplus  approaches  or  is  attracted  towards  another 
which  is  undercharged — in  other  words,  if  a cloud  posi- 
tively electrified  approaches  one  negatively  electrified — 
the  surplus  flashes  from  the  one  into  the  other  in  the  form 
of  lightning,  with  a noise  stunning  to  the  ear.* 

ATTRACTION  OF  GRAVITATION. 

60.  As  the  attraction  of  cohesion  unites  the  particles 
of  matter  into  masses  or  bodies,  so  the  attraction  of  gravi- 
tation tends  to  force  those  masses  towards  each  other,  to 
form  others  of  still  greater  dimensions. 

61.  The  force  of  attraction  increases  in  proportion  as 
bodies  approach  each  other,  and  by  the  same  law  it  must 
diminish  in  proportion  as  they  recede  from  each  other. 

62.  Attraction,  in  technical  language,  is  inversely  as 
the  squares  of  the  distances  between  the  two  bodies. 
That  is,  in  proportion  as  the  square  of  the  distance  in- 
creases, in  the  same  proportion  attraction  decreases,  and 
so  the  contrary.  Thus,  if  at  the  distance  of  2 feet,  the 
attraction  be  equal  to  4 pounds,  at  the  distance  of  4 feet 
it  will  be  only  1 pound ; for  the  square  of  2 is  4,  and  the 
square  of  4 is  16,  which  is  4 times  the  square  of  2.  On 
the  contrary,  if  the  attraction  at  the  distance  of  6 feet  be 
3 pounds,  at  the  distance  of  2 feet  it  will  be  9 times  as 
much,  or  27  pounds,  because  36,  the  square  of  6,  is  equal 
to  9 times  4,  the  square  of  2. 

63.  The  intensity  of  light  is  found  to  increase  and  di- 
minish in  the  same  proportion.  Thus,  if  a board  a foot 
square  be  placed  at  the  distance  of  one  foot  from  a candle, 
it  will  be  found  to  hide  the  light  from  another  board  of 
two  feet  square,  at  the  distance  of  two  feet  from  the  can- 
dle Now,  a board  of  two  feet  square  is  just  four  times 
as  large  as  one  of  one  foot  square,  and  therefore  the  light 
at  double  the  distance  being  spread  over  four  times  the 
surface,  has  only  one-fourth  the  intensity. 

* Fur  a further  account  of  Magnetism  and  Electricity,  see  trea 
tises  on  these  branches  of  Natural  Philosophy. 


48.  Define  attraction  of  gravitation,  and  its  laws. 

49.  What  of  the  laws  of  the  intensity  of  light? 


ATTRACTION  OF  GRAVITATION. 


25 

(54.  The  gradual  diminution  of  attraction,  as  the  dis- 
tance increases,  is  exemplified  in  the  following  table.  In 
the  upper  line,  the  distance  is  expressed  by  progressive 
numbers  ; in  the'  lower  corresponding  squares,  the  dimi- 
nution of  attraction  is  indicated  by  the  common  arithme- 
tical fractions. 


Distance 

2 

3 

4 

5 

6 

7 

8 

and  so  on. 

1 

1 Attraction 

i 

1 

J_ 

4 

1_ 

9 

16 

25 

36 

49 

64 

and  so  on. 

It  is  here  seen,  that,  at  the  distance  of  8,  the  attractive 
force  is  diminished  to  a sixty-fourth  part  of  what  it  was 

at  1. 

(55.  The  attractive  force  of  matter  is  also  in  proportion 
to  the  numbers  of  the  atoms  of  matter  which  a body  con- 
tains ; the  attraction  therefore  does  not  proceed  from  the 
mere  surface  of  a body,  but  from  all  the  particles  which 
individually  compose  it. 

t56.  Some  bodies  of  the  same  bulk  contain  a much 
greater  quantity  of  matter  than  others:  thus,  a piece  of 
lead  contains  about  twelve  times  as  much  matter  as  a 
piece  of  cork  of  the  same  dimensions  ; and  therefore  a 
piece  of -lead  of  any  given  size,  and  a piece  of  cork 
twelve  times  as  large,  will  attract  each  other  equally. 

(57.  The  attractive  power  of  any  mass  acts  from  the 
centre.  At  all  equal  distances  from  the  centre,  the  at- 
tractive power  is  equal  ; for  instance,  in  a body  per- 
fectly spherical,  the  attraction  to  the  centre  would  be  the 
same  at  all  parts  of  the  surface.  The  distance  of  the  cen- 
tre of  a sphere  from  its  surface  is  called  the  semi-diame/ei 
of  that  sphere — that  is,  the  half  of  its  thickness.  At  a 
point  as  far  from  the  surface  of  a sphere  as  its  semi- 
diameter, its  attractive  power  is  diminished  to  a fourth. 
At  three  distances,  the  attraction  is  a ninth  ; at  four  dis- 


50.  Explain  the  table. 

51.  What  of  the  number  of  atoms  of  a body  f 

52.  What  differences  between  bulk  and  quantity  ? 

53.  How  does  the  centre  of  attraction  vary  ? 


28 


ATTRACTION  OF  GRAVITATION. 


tances,  a sixteenth  ; and  so  on.  When  we  wish,  therefore, 
to  ascertain  the  relative  amount  of  the  attraction  which  any 
mass  of  matter  exercises  over  another,  the  rule  is,  to  inquire 
how  many  semi-diameters  of  the  one  the  other  is  distant 
from  it,  and  then  to  multiply  that  number  by  itself.  The 
result  shows  how  many  times  the  attraction  at  this  distance 
is  less  than  at  the  surface  of  the  former.  The  moon,  for 
instance,  is  distant  240,000  miles  from  the  earth ; or  as 
much  as  60  semi-diameters  of  the  earth  ; 60  multiplied  by 
60  gives  3600  ; consequently,  the  attraction  exercised  by 
the  earth  upon  the  moon  is  a 3000th  part  of  what  it  would 
exercise  upon  th  • same  mass  at  its  own  surface. 

68.  If  the  earth  were  a perfectly  spherical  body,  its 
attraction  would  be  equal  everywhere  at  the  level  of  the 
sea.  As  the  surface  at  the  pole  is  thirteen  miles  nearer 
the  centre  than  the  surface  at  the  equator,  the  attraction 
is  stronger  at  the  former  than  at  the  latter  place  ; it  gets 
proportionally  weaker  as  we  advance  towards  the  equator, 
on  account  of  the  increase  of  distance  from  the  centre. 
Hence,  a mass  of  iron  which  is  considered  a pound  weight 
in  Britain,  would  be  Jess  than  a pound  on  the  coast  of 
Guinea,  and  more  than  a pound  in  Greenland,  for  weight 
is  only  a result  of  attraction.  If  we  ascend  a mountain, 
the  effect  is  the  same  as  if  we  proceed  towards  the  equa- 
tor: we  are  always  getting  farther  from  the  centre  of  attrac- 
tion, and  consequently  weights  become  lighter.  On  the 
top  of  a hill  four  miles  high,  a ball  of  four  thousand 
pounds’  weight  would  be  found  to  be  two  pounds  lighter. 

69.  Pressure  downwards,  or  weight,  is  in  philosophical 
language  termed  gravity,  and  under  that  head  it  is  here- 
after treated,  in  connection  with  the  phenomena  of  falling 
bodies. 

70.  In  the  set  of  large  spheres  constituting  the  Solar 
System,  the  Sun  is  a central  body  of  vast  size,  while  the 
Planets  are  comparatively  small  bodies,  revolving  round 
him  at  different  distances.  If  we  take  a stone  in  a sling, 
and  whirl  it  round,  the  stone  will  have  a tendency,  in  the 

54.  By  what  rule  is  relative  attraction  found  ? 

55.  How  illustrated  with  the  moon  ? 

56.  Why  does  weight  diminish  toward  the  equator  ? 


ATTRACTION  OF  GRAVITATION. 


27 


event  of  our  slipping-  the  string,  to  fly  off  in  a straight 
line.  This  is  called  Centrifugal  Force,  that  is,  a force 
operating  so  as  to  cause  a body  to  fly  from  a centre. 
When  tb»  planets  received  their  first  impulse,  they  had 
the  same  tendency  as  a stone  in  a sling  to  fly  off  in  a 
straight  tine  into  space;  in  which  case,  they  would  never 
have  come  to  a stop,  till  they  fell  under  the  attractive  in- 
fluence of  some  body  of  sufficient  mass.  But  while  im- 
pelled thus  to  fly  off  from  the  sun,  they  were  also  under 
the  influence  of  his  attraction,  which,  in  this  instance,  is 
called  Centripetal  Force — that  is  a force  impelling  a mass 
to  seek  nr  go  to  a centre.  At  once  impelled  from  the 
sun  by  their  original  motion,  and  drawn  to  him  by  his  at- 
traction, they  took  what  may  be  called  a middle  course, 
and  began  to  revolve  round  him  at  mean  distances  adapted 
to  their  rates  of  speed,  and  the  force  of  the  sun’s  attrac- 
tion. The  same  laws  caused  the  satellites  to  revolve  at 
certain  distances  round  the  planets. 

71.  The  attraction  of  bodies  is  mutual,  and  in  propor- 
tion to  the  quantity  of  matter  they  contain.  Therefore, 
any  body,  however  small,  exerts  some  degree  of  attrac- 
tion upon  the  mass  of  the  earth.  Any  body  which  comes 
immediately  under  our  observation,  is  so  small  in  compa- 
rison to  the  earth,  that  its  attractive  force  is  altogether  un- 
appreciable  ; but  if  the  body  were  of  great  density,  and 
of  dimensions  approaching  to  those  of  the  earth,  then  we 
should  see  the  earth  rise  to  meet  the  body,  or  fall  towards 
the  body.  The  heavenly  bodies,  when  they  approach 
each  other,  are  drawn  out  of  the  line  of  their  paths,  or 
orbits,  by  mutual  attraction. 

72.  It  is  found  by  experiment,  that  a plumb-line  sus- 
pended in  the  neighbourhood  of  a mountain,  is  sensibly 
attracted  towards  the  mountain  from  the  true  vertical  line. 

72.  The  mutual  attraction  of  matter  is  exemplified  by 
the  diminution  of  the  weight  of  bodies,  as  we  penetrate 
into  the  earth.  At  the  depth  of  a mile,  a body  weighing 


57.  Explain  centrifugal  and  ceniripetal  forces. 

58.  How  is  the  revolution  of  the  planets  perpetuated  ? 

59.  How  is  the  attraction  of  a mountain  shown  ? 

60.  What  change  in  gravity  by  nearing  the  centre  of  the 


28 


ATTRACTION  OF  GRAVITATION. 


a pound  would  be  found  to  be  lighter  than  at  the  surface. 
This  is  in  consequence  of  the  attraction  of  the  matter  of 
the  shell  of  the  earth,  which  is  exterior  to  the  point,  being 
nothing,  in  consequence  of  the  attractions  of  its  particles 
on  this  point  counteracting  each  other ; and  hence  the 
only  efficient  attraction  on  it  arises  merely  from  the  smaller 
sphere  below  the  point,  and,  therefore,  the  nearer  the  point 
is  to  the  centre,  the  less  is  this  internal  sphere  ; and  the 
less  therefore  is  its  attraction  on  the  point. 

74.  Were  we  to  proceed  to  the  centre  of  the  earth,  we 
should  there  find  that  weight  altogether  ceased,  because 
the  attractive  power  would  be  equal  on  all  sides.  Were 
there  a cavity  at  the  earth’s  centre,  the  body  would  hang 
suspended  in  space. 

75.  The  attraction  of  the  earth’s  mass  performs  an  im- 
portant function,  in  binding  the  atmosphere,  which  is  an 
elastic  fluid,  around  the  surface  of  our  planet,  and  of  caus- 
ing the  air  to  perforate  every  open  crevice  and  pore  in  the 
superficial  substances  of  the  globe.  The  attractive  force, 
in  this  respect,  produces  what  is  called  atmospheric  pres- 
sure, the  air  being  pulled  or  pressed  down  by  a force  equi- 
valent to  about  15  lbs.  on  the  square  inch,  at  the  level  of 
the  sea,  and  diminishes  in  proportion  to  the  distance  above 
that  common  level.  The  degree  of  atmospheric  pressure 
at  any  given  height  is  ascertained  by  an  instrument  called 
the  barometer , which  consists  of  a column  of  mercury  in 
a tube,  and  by  the  pressure  of  the  air  upon  which,  the 
height  above  the  level  of  the  sea  may  be  judged.* 

70.  Atmospheric  pressure  is,  then,  a result  of  attraction, 
and  as  such  produces  divers  phenomena  in  nature.  It  is 
possible,  by  artificial  means,  to  draw  out  the  air  from  a 
confined  vessel,  as  in  the  case  of  the  air-pump  and  its  re- 
ceiver, so  as  to  produce  a vacuum,  or  almost  perfect  ab- 
sence of  air  and  its  pressure  ; but  it  is  not  possible  to  di- 
minish in  any  way  the  attraction  of  gravitation,  which  is 
a property  inherent  and  indestructible  in  all  matter. 

* See  treatise  on  Pneumatics. 


61.  What  effect  has  gravitation  upon  the  air? 

62.  Name  the  average  lorce  of  this  pressure. 

63.  What  instrument  measures  relative  pressure  ? 


REPULSIVE  QUALITY  IN  MATTER HEAT. 


29 


77.  Some  bodies  do  not  appear  to  be  affected  by  attrac- 
tion ; for  instance,  smoke  and  vapours  rise,  instead  of  fall- 
ing to  the  ground;  in  all  such  cases,  however,  attraction 
is  present.  Smoke  consists  chiefly  of  condensed  vapour 
and  minute  particles  of  soot,  and  is  carried  upwards  by  the 
impulse  of  an  ascending  current  of  air,  which  is  warmer, 
and  therefore  lighter,  than  the  surrounding  atmosphere. 
The  sooty  particles  soon  descend  again,  and  the  vaporous 
particles  are  commonly  dissolved  by  the  atmosphere, 
forming  a transparent  solution,  and  thus  becoming  invi- 
sible. 

THE  REPULSIVE  QUALITY  IN  MATTER— HEAT.* 

78.  While  “attraction  tends  to  unite  and  compress  the 
particles  of  matter,  there  is  another  and  equally  universal 
principle,  known  in  familiar  language  by  the  appellation 
of  Heat,  the  tendency  of  which  is  to  keep  the  particles  of 
matter  at  a certain  degree  of  expansion.  Heat  is  often, 
in  scientific  works,  named  caloric,  from  the  Latin  word  for 
heat. 

79.  Heat  pervades  ail  things,  but  some  in  greater  de- 
grees than  others.  Even  ice  has  been  found  to  contain  a 
certain  portion  of  heat.  In  fact,  there  is  no  such  thing  in 
nature  as  positive  cold.  The  things  which  seem  cold  to 
us,  are  only  under  a low  degree  of  heat. 

80.  The  absolute  nature  of  this  universal  principle  is  un- 
known. We  only  know  it  by  its  effects,  and  the  sensa- 
tions it  produces.  Some  have  conjectured  that  it  is  a fluid  ; 
others  think  it  is  a quality  or  affection  of  matter,  resulting 
from  electrical  action.  From  its  producing  no  sensible 
difference  in  the  weight  of  any  substance,  it  has  been  called 
an  imponderable  body. 

* The  operations  and  properties  of  Heat  form  a branch  of  know- 
ledge sometimes  called  Pyronomics,  a word  signifying  the  Laws  of 
Fite. 


64.  How  is  gravitation  proved  without  the  air? 

65.  How  is  the  ascent  of  smoke  and  vapour  explained  ? 

66.  What  principle  in  matter  produces  repulsion  ? 

67.  What  of  heat  and  of  cold  ? 

68.  By  what  name  is  it  designated  ? 


SO  REPULSIVE  QUALITY  TV  MATTER HEAT. 

81.  When  the  heat  of  any  particular  substance,  as  ice, 
stone  or  wood,  is  not  sensible  to  us,  it  is  called  latent  that 
is,  concealed)  heat.  We  may  very  readily  detect  its  pre- 
sence in  a piece  of  wood  or  metal  by  rubbing  or  friction. 
If  a button,  for  instance,  be  rubbed  on  a table,  it  will  soon 
become  too  hot  to  be  held  by  the  fingers.  In  like  manner, 
the  axle  of  any  carriage-wheel  soon  becomes  hot,  unless 
the  friction  is  prevented  by  grease. 

82.  Heat,  in  its  extreme  form  becomes  fire.  Thus,  if  an 
ungreased  wheel  be  rapidly  turned  for  a long  time  on  its 
axle,  so  much  heat  will  be  excited  that  both  wheel  and 
axle  will  burst  into  a flame.  The  effects  of  powerful  fric- 
tion are  known  to  savage  nations,  among  whom  it  is  com- 
mon  to  produce  fire  by  rubbing  two  sticks  together. 

83.  Two  pieces  of  flint  struck  together,  or^.  flint  struck 
hard  upon  a piece  of  iron,  evolve  sparks  of  fire.  By  such 
means,  many  important  purposes  are  served  ; for  instance, 
the  discharge  of  fire-arms.  Fire  can  also  be  evolved  from 
the  common  atmosphere,  by  compressing  a quantity  of  it 
suddenly  in  a tube, -at  the  bottom  of  which  a piece  of  tinder 
has  been  placed. 

84.  The  evolution  of  heat  by  these  means,  and  other 
circumstances,  lead  to  the  conclusion  that  heat  is  an 
element  mixed  up  with  the  atoms  of  matter,  which  it 
serves  to  keep  at  a lesser  or  greater  distance  from  each 
other.  Thus,  as  we  squeeze  the  pores  of  a sponge  toge- 
ther, and  disengage  the  liquid  which  they  held  in  cohesion, 
so,  when  squeezing  or  rubbing  a portion  of  matter,  do  we 
disengage  the  heat  which  it  retained  amongst  its  compo- 
nent atoms. 

85.  In  all  cases  of  the  development  of  heat  by  pressure, 
hammering,  and  friction,  the  cause  is  the  squeezing  to- 
gether of  atoms  which  nad  been  kept  asunder  by  the  latent 
fluid,  and  which  fluid  must,  as  a matter  of  necessity,  come 
forth  and  make  itself  sensibly  felt  or  seen. 


69.  What  is  meant  by  latent  heat  ? and  how  detected  ? 

70.  In  what  ways  is  artificial  fire  produced  i 

71.  How  is  this  explained  ? 

72.  What  are  the  two  great  antagonist  powers  f 

73.  Of  what  use  are  these  opposing  agents  ? 


REPULSION  AND  CONDUCT! ON  OF  HEAT. 


31 


REPULSIVE  QUALITY  OF  HEAT. 

86.  Heat,  then,  is  a principle  of  Repulsion  in  nature, 
and  in  this  capacity  its  uses  are  as  obvious  as  those  of  ter- 
restrial gravitation,  to  which  it  apparently  acts  as  a coun- 
terpoise. The  force  of  attraction  is  so  powerful,  that  un- 
less for  a counteracting  principle  of  repulsion,  all  bodies 
would  hasten  into  close  contact ; there  would  be  no  air,  no 
water,  no  vegetable  or  animal  life  ; all  would  be  a uniform 
dead  solid  mass,  and  the  earth  itself  might  perhaps  be  re- 
duced to  a small  portion  of  its  present  bulk. 

MODIFYING  QUALITY'  OF  HEAT. 

87.  Heat,  by  pervading  all  things,  modifies  attraction, 
and,  according  to  circumstances,  regulates  the  density  or 
solidity  of  bodies.  Hence  we  possess  in  nature  a beauti- 
ful variety  of  substances,  some  solid  and  hard,  like  stone 
and  marble  ; others  soft,  or  of  the  jelly  form  ; a third  class 
liquid,  like  water;  and  a fourth  kind  aeriform,  or  gaseous. 
Heat  expands  most  bodies  in  proportion  as  it  is  increased 
in  quantity,  and  they  become  solid  in  proportion  as  it  is 
withdrawn.  Water  may  thus  be  either  expanded  into  the 
form  of  vapour  or  steam,  or  hardened  into  ice.  When 
withdrawn,  the  process  of  cooling  is  said  to  take  place  ; 
cold  being  simply  a state  of  abstraction  or  comparative  ab- 
sence of  heat. 


CONDUCTION  OF  HEAT. 

88.  Heat  is  diffused  or  communicated  by  conduction 
and  radiation.  When  it  passes  slowly  from  one  portion 
of  matter  to  another  in  contact  with  it,  it  is  said  to  be  con- 
ducted ; and  the  process,  in  scientific  language,  is  termed 
the  conduction  of  caloric.  Metals  are  the  best  conductors, 
then  liquids,  and,  lastly,  gases.  Gold,  silver,  and  copper, 
are  the  best  conductors  among  solids : glass,  bricks,  and 
many  stony  substances,  are  very  bad  conductors ; and 


74.  How  does  heat  modify  bodies  ? 

75.  What  variety  in  nature  is  thus  explained  ? 

76.  Name  the  illustrations. 

77.  How  is  heat  diffused  ? illustrate  this. 


32  RADIATION  AND  PRODUCTION  OF  HEAT. 

porous  spongy  substances,  as  charcoal,  hair,  and  fur,  are 
the  worst. 

89.  Clothing  is  generally  made  of  bad  conductors,  that 
the  heat  of  the  body  may  not  be  conducted  quickly  to  the 
surrounding  air.  Furnaces,  where  great  heat  is  required, 
are  built  with  porous  bricks,  which  are  very  effectual  in 
preventing  the  escape  of  heat,  and  do  not  readily  commu- 
nicate the  fire  to  adjacent  bodies. 

RADIATION  OF  HEAT. 

90.  Heat  is  said  to  radiate,  when  it  is  emitted  from  a fire 
or  from  the  rays  of  the  sun,  and  affects  the  atmosphere  or 
substances  at  a distance  from  its  source.  Radiant  heat  is 
absorbed  when  it  falls  upon  bodies  having  painted  or  rough 
surfaces,  such  as  are  presented  by  bricks  and  other  porous 
solids,  by  many  kinds  of  stony  matter,  and  numerous  ani- 
mal and  vegetable  substances,  and  makes  them  wanner 
as  it  is  taken  up.  But  brilliant  and  polished  metallic 
surfaces  absorb  little  heat ; they  reflect  or  turn  it  back 
again. 


PRODUCTION  OF  HEAT. 

91.  Heat,  as  already  mentioned,  can  be  brought  into 
action  in  most  substances,  by  percussion  and  rubbing.  It 
is  also  produced  by  the  burning  of  certain  inflammable 
substances,  as  coal  and  wood  : and  in  this  manner  its  chief 
purposes  in  domestic  economy  are  effected.  But  the  most 
remarkable  source  of  heat  is  the  sun  ; though  whether  this 
luminary  is  a burning  mass,  throwing  off  warmth  like  a 
common  fire  or  red-hot  ball,  or  produces  the  effect  by 
some  peculiar  and  unknown  operation,  is  as  yet  un- 
certain. 

92.  Heat,  besides  being  produced  by  the  sun’s  rays, 
and  by  the  friction  and  combustion  of  inanimate  substances, 
is  evolved  by  chemical  action,  a familiar  example  of  which 
is  observable  in  fermentation.  It  is  by  means  of  a natural 
chemical  action  in  connection  with  the  circulation  of  the 


78.  Define  and  illustrate  radiation. 

79.  Name  the  sources  of  heat. 

80.  Give  examples  of  the  chemical  production  of  heat. 


DISTRIBUTION  OF  HEAT THE  THERMOMETER.  33 

blood,  that  heat  is  resident  and  sustained  in  most  living 
animals.  A stoppage  of  the  circulation  of  the  blood,  as 
every  one  knows,  leads  to  an  absence  of  animal  heat,  or 
a very  considerable  degree  of  coldness.  On  the  contrary, 
quick  circulation  of  the  blood,  and  active  muscular  motion, 
as  well  as  rubbing,  produce  heat.  In  these  cases  of  mo- 
tion and  rubbing  the  heat  seems  to  be  in  a great  mea- 
sure evolved  by  the  momentary  compression  of  the 
parts. 

GENERAL  DISTRIBUTION  OF  HEAT. 

93.  Heat  is  unequally  distributed  over  the  globe.  At 
and  near  the  equator,  where  the  rays  of  the  sun  are  sent 
in  the  greatest  degree  of  directness,  the  greatest  heat  pre- 
vails. In  the  parts  of  the  earth  adjacent  to  the  north  and 
south  poles,  he  transmits  his  rays  so  slantingly  as  to  have 
little  power  ; and  there,  accordingly,  the  air  is  seldom  of 
a genial  mildness.  The  higher  we  ascend  in  the  air,  the 
colder  it  becomes  ; the  summits  of  very  high  mountains 
are  always  covered  with  snow.  In  penetrating  into  the 
body  of  the  earth,  after  gaining  a certain  depth,  the  heat 
becomes  greater  in  proportion  as  we  descend.  The  inte- 
rior of  the  globe  is  by  many  believed  to  be  at  a very  ele- 
vated degree  of  heat,  if  not  in  a state  of  ignition.  On  the 
surface,  great  expanses  of  sea  tend  to  equalize  and  temper 
the  degrees  of  heat  and  cold  in  their  neighbourhood,  and 
great  continents  have  the  contrary  effect. 

TEMPERATURE THE  THERMOMETER. 

94.  The  degrees  of  heat  and  cold  in  the  atmosphere  are 
called  its  temperature  ; and  for  ascertaining  this  correctly, 
with  reference  to  a standard,  a very  ingenious  instrument 
has  been  invented.  This  is  called  the  thermometer  (a 
word  signifying  heat  measurer).  It  is  a glass  tube  with  a 
bulb  at  the  bottom,  into  which  mercury  or  quicksilver  is 
put,  with  a scale  of  figures  along  the  tube  to  mark  the 
lising  of  the  quicksilver.  This  instrument  differs  from 

8) . What  of  the  distribution  of  heat  ? 

82.  Name  causes  of  its  inequality. 

83.  What  of  temperature  and  its  measurement  7 ' 


34 


TEMPERATURE-— THE  THERMOMETER. 


the  barometer,  inasmuch  as  the  quicksilver  is  sealed  up 
close  from  the  air.  The  atmospheric  heat,  however,  affects 
the  metallic  fluid  in  the  bulb,  and,  according  to  its  warmth, 
causes  it  to  expand  and  rise  in  the  tube.  The  degree 
of  temperature  is  indicated  by  the  figures  to  which  it  as- 
cends. 

95.  Our  common  thermometer  has  a graduation  from 
No.  1,  near  the  bulb,  to  212,  the  degree  of  heat  of  boiling 
water.  In  the  scale  of  figures,  32  is  marked  as  the  freez- 
ing point— that  is  to  say,  when  the  mercury  is  at  the 
height  of  32,  water  freezes  ; and  the  more  it  is  below  that 
point,  the  more  intense  is  the  frost.  55  is  reckoned  mode- 
rate heat,  and  76  summer  heat,  in  Great  Britain.  98  is 
the  heat  of  the  blood  in  the  average  of  living  men.* 

96.  The  rising  of  mercury  in  the  tube  of  the  thermo- 
meter offers  a familiar  example  of  the  repulsive  power  of 
heat  in  expanding  or  dilating  bodies.  Common  experience 
affords  many  such  examples.  A bar  of  iron  is  longer  and 
thicker  when  hot  than  when  it  is  cold.  The  iron  rim  of 
a wheel  slips  easily  into  its  place  when  hot,  and  gripes  or 
binds  fast  when  it  becomes  cool.  When  heated  from  32 

* Different  nations  adopt  different  graduations  in  the  scale  of  ther- 
mometers, which  is  a fertile  source  of  error  and  confusion  in  estimating 
and  comparing  the  statements  of  temperature  made  by  scientific  men 
in  different  countries.  Where  ever  the  English  language  prevails,  the 
graduation  of  a person  called  Fahrenheit  is  generally  preferred.  By 
the  Germans,  Reaumur’s  is  used;  and  the  French  now  adopt  what 
they  term  a centigrade  thermometer.  In  the  French  centigrade  ther- 
mometer, 0 is  the  freezing  point,  and  100  the  boiling  point  ; in  Reau- 
mur’s thermometer,  0 is  the  freezing  point,  and  80  the  boiling  point. 
Each  degree  of  Reaumur  is  equal  to  two  and  one-fourth  of  Fahrenheit. 
[Of  course  this  rule  can  only  be  accurately  applied  by  adding  the  dif- 
ference of  32°  in  all  c mparisons  between  these  two  scales,  the  zero 
of  Fahrenheit  being  32°  below  the  zero  of  Reaumur.]  It  was  at  one 
time  imagined  that  the  greatest  cold  could  make  the  fluid  in  the  ther- 
mometer fall  only  32°  below  the  freezing  point,  the  place  to  which  it 
then  fell  being  zero , and  therefore  the  noation  commenced  at  that 
place.  But  much  greater  degrees  of  cold  exist  at  different  parts  of  our 
globe  in  winter,  and  may  be  produced  artificially,  so  that  the  fluid  in 
the  stem  of  the  thermometer  ofien  descends  below  that  point,  and  is 
then  said  to  be  at  so  many  degrees  below  zero.  Thermometers  in 
common  use,  however,  are  not  made  with  a stem  and  indications  below 
zero. 


84.  Describe  this  instrument. 


REPULSIVE  ENERGY BOILING  WATER. 


35 


to  212,  air  expands  3-Sths  of  its  volume,  alcohol  l-9th, 
water  l-22d,  and  hammered  iron  l-273d.  In  these,  and 
all  similar  instances,  the  expansion  arises  from  the  fluid  of 
heat  lodged  among  the  atoms  of  matter  pressing  outwards 
on  all  sides  according  as  it  is  excited. 

REPULSIVE  ENERGY BOILING  WATER. 

97.  The  repulsive  energy  of  heat  is  strikingly  exem- 
plified in  the  explosion  of  gunpowder.  The  particles  of 
powder  on  being  ignited,  and  assuming  the  form  of  air, 
are  repelled  with  a force  sufficient  to  lift  immensely 
heavy  bodies,  and  to  project  shot  to  a distance  of  several 
miles. 

98.  The  repulsive  energy  of  heat  is  also  observable  in 
the  case  of  boiling  water.  When  water  is  placed  in  a 
vessel  on  the  fire,  its  particles  become  gradually  heated. 
Those  nearest  the  fire  are  heated  first ; being  then  of  a 
lighter  or  more  expanded  nature,  they  hasten  or  are  re- 
pelled to  the  surface,  while  the  more  cold  and  heavy  par- 
ticles sink  downwards  to  the  bottom,  and  are  heated  in 
turn.  In  this  manner  the  process  of  heating  proceeds, 
until  all  the  particles  are  of  a uniform  temperature. 
There  is  a limit  beyond  which,  in  ordinary  circumstances, 
they  cannot  be  heated.  This  is  when  the  water  boils,  and 
is  signified  by  the  bubbling  motion  of  the  fluid.  Boiling 
takes  place,  as  above  mentioned,  when  the  water  readies 
212  degrees  in  the  thermometer.  Nature  has  designed 
that  water  should  not  become  hotter  by  continued  boiling, 
the  application  of  heat  after  reaching  this  point  being  ex- 
pended in  transforming  the  liquid  into  vapour  or  steam. 
Hence  it  is  not  economical  to  boil  any  substance  quickly 
which  may  onty  require  exposure  to  a boiling  temperature, 
as  all  the  heat  that  may  be  consumed  in  producing  vapour 
must  cause  an  unnecessary  expenditure  of  fuel. 

99.  The  temperature  of  212,  at  which  water  boils,  is 
only  reached  when  the  ordinary  atmospheric  pressure  is 


85.  What  examples  ol  the  repulsion  of  heat  are  cited  ? 

86.  N ame  the  illustrations  g.ven  of  the  force  of  repulsion. 

87.  How  is  this  illustrated  by  boiling  water  ? 

88.  Does  water  become  hotter  by  continuing  the  boiling  ? 


VAPORIFIC  POINT STEAM. 


Q i» 

ou 

allowed  to  influence  it.  If  the  pressure  be  diminished  or 
entirely  removed  by  the  air-pump,  the  water  will  boil  or 
fly  off  in  the  vapour  form  at  a much  lower  temperature. 
At  the  summit  of  high  mountains,  where  the  pressure  of 
the  atmosphere  is  less  than  at  the  common  level  of  the 
surface  of  the  earth,  water  boils  at  a lower  temperature 
than  212.  Thus,  at  the  summit  of  Mount  Blanc,  the 
highest  peak  of  the  Alps,  which  is  15,666  feet  above  the 
level  of  the  sea,  it  has  been  found  that  water  boils  at  187 
degrees  of  the  thermometer,  or  25  degrees  below  the  ordi- 
nary boiling  point. 

100.  An  interesting  experiment  may  be  performed  with 
the  view  of  exhibiting  the  boiling  of  water  under  the  influ- 
ence of  a light  pressure.  Take  a thin  glass  vessel,  con- 
taining a quantity  of  water ; hold  it  over  a flame  till  it 
boils,  and  then  briskly  and  securely  cork  it,  and  remove  it 
from  the  flame  so  as  to  let  it  cool.  It  will  at  first  cease  to 
boil,  but  the  vapour  will  soon  be  condensed  so  as  to  form 
a vacuum.  By  this  means  atmospheric  pressure  is  par- 
tially removed,  and  the  water  again  begins  to  boil.  By 
pouring  cold  water  on  the  vessel,  the  vacuum  will  become 
greater,  and  the  boiling  will  become  more  violent.  When 
at  this  stage  in  the  process,  pour  boiling  water  on  the  ves- 
sel, and  the  vapour  will  again  rise  and  fill  the  vacuum,  so 
as  to  apply  the  pressure  which  was  originally  possessed, 
and  the  boiling  will  cease,  but  may  he  again  commenced 
by  a second  application  of  cold  water. 

VAPORIFIC  POINT STEAM. 

101.  Different  liquids  reach  the  boiling  or  vaporific 
point  at  different  degrees  of  temperature.  AEther  becomes 
vapour  at  10 1 degrees,  alcohol  or  spirits  at  175,  water  at 
212,  and  mercury  at  602. 

102.  Steam  is  transparent,  colourless,  and  invisible  like 
the  air.  The  white  cloudy-looking  matter  which  is  emit- 

sy.  What  becomes  of  the  superfluous  heat  ? 

yo.  How  is  the  boiling  point  of  liquids  affected  by  the  atmospheric 
pressure  ! and  how  is  this  shown  ? 

91.  What  simple  experiment  exhibits  the  differences  ? 

92.  What  of  the  boiling  point  of  liquids  ? 

93  Des'-nbe  s eam,  and  ihe  extent  of  the  expansion. 


SPONTANEOUS  EVAPORATION. 


37 


ted  in  the  form  of  vapour,  is  moisture  produced  by  the 
partial  condensation  of  the  steam  in  the  atmosphere.  A 
cubic  inch  of  water  produces  almost  exactly  a cubic  foot  of 
steam,  or  1728  cubic  inches.  In  proportion  as  we  increase 
the  heat  which  produces  steam,  and  do  not  suffer  it  to 
escape,  so  do  its  repulsive  properties  become  more  appa- 
rent. It  will  burst  the  strongest  vessels  in  which  it  may 
be  generated  or  confined.  When  the  force  with  which  it 
expands  is  carefully  regulated,  so  as  to  produce  motion  in 
machinery,  it  forms  the  most  powerful  engine  which  man 
has  invented,  namely,  the  steam-engine. 

103.  When  steam  is  exposed  to  cold,  it  condenses  into 
water,  giving  out  all  the  heat  by  which  it  was  produced  ; 
and  hence  the  severe  scald  it  produces  when  condensed  on 
any  part  of  the  body. 

104.  Distillation  consists  in  the  production  of  vapour  by 
heat ; the  spirituous  particles  of  the  liquid  are  carried  off 
and  condensed,  by  passing  through  a tube  immersed  in  cold 
water. 

SPONTANEOUS  EVAPORATION. 

105.  Spontaneous  evaporation  is  the  term  usually  em- 
ployed when  vapour  is  produced  slowly  from  a fluid,  and 
without  ebullition,  as  when  water  disappears  from  any 
moist  surface.  Evaporation,  to  a lesser  or  greater  extent, 
is  in  constant  exercise  over  the  whole  earth.  The  ocean, 
lakes,  rivers,  fields,  are  ever  yielding  up  water  in  this  in- 
visible form  to  the  atmosphere  ; and  plants  and  vege- 
tables, as  well  as  living  creatures,  are  also  giving  forth  ex- 
halations. 

106.  The  atmosphere  is  thus  a great  receptacle  for  the 
moisture  of  the  earth.  When  the  temperature  of  the  air 
is  high,  moisture  in  the  atmosphere  is  not  generally  per- 
ceptible near  the  ground.  But  when  the  temperature  is 
low,  the  air  is  felt  to  be  damp  or  humid,  in  which  condi- 
tion it  is  unwholesome.  Sometimes  the  humidity  becomes 


94.  Explain  the  effects  and  manner  of  condensing  steam. 

95.  What  of  distillation  ? 

96  Explain  spontaneous  evaporation,  wiih  examples. 

97  What  natural  phenomena  depend  upon  it  ? 


38 


FROST FREEZING  POINT. 


so  great,  that  the  watery  particles  in  the  atmosphere  are 
observable  in  the  form  of  mist  or  fog.  At  night,  when  the 
plants  lose  their  heat  which  they  have  contracted  during 
the  day,  the  moisture  of  the  atmosphere  is  condensed  upon 
them  in  the  shape  of  dew,  which,  in  very  cold  nights,  be- 
comes hoar-frost.  When  aqueous  vapours  are  carried 
high  into  the  atmosphere,  or  are  formed  there,  they  receive 
the  name  of  clouds. 

107.  The  invisible  steam  or  vapour  constantly  arising 
from  the  pores  in  the  skin  of  living  animals,  and  exhaled 
in  breath  from  the  lungs,  may  be  observed  to  condense  into 
liquid  on  the  insides  of  panes  of  glass  in  windows,  and  on 
the  walls  of  apartments.  This,  however,  only  occurs  when 
the  walls  are  comparatively  cold,  or  when  the  outer  atmo- 
sphere affecting  the  glass  is  colder  than  the  atmosphere 
within  ; and  in  proportion  to  the  degree  of  external  cold, 
so  is  the  condensation  and  deposition  of  liquid  greater. 

FROST FREEZING  POINT. 

108.  When  the  temperature  of  the  atmosphere  falls  be- 
low the  freezing  point,  32,  which  it  does  principally  from 
the  weakness  of  the  sun’s  rays  in  winter,  the  phenomenon  of 
frost,  or  freezing,  ensues.  Freezing  is  a process  of  conge- 
lation, or  properly  crystallization,  produced  by  the  with- 
drawal of  heat,  and  by  which  water  assumes  the  form  of 
ice.  When  the  temperature  of  the  atmosphere  rises  above 
the  freezing  point,  the  ice  melts,  and  is  resolved  into  its 
original  element. 

109.  When  the  temperature  of  the  atmosphere  is  be- 
low the  freezing  point,  the  particles  of  water  which  are 
upheld  in  the  clouds  are  frozen  in  their  descent,  and  reach 
the  earth  in  the  form  of  flakes  of  snow.  If  this  freezing 
take  place  after  the  particles  have  become  united  into  rain- 
drops, we  have  hail  instead  of  snow.  When  the  descend- 
ing flakes  of  snow  come  into  a temperature  above  the  freez- 
ing point  as  they  approach  the  earth,  they  are  apt  to  melt, 


98.  What  familiar  example  of  condensed  vapour  is  cited? 
99  Explain  freezing,  snow,  hail,  sleet,  &c. 

100.  Describe  equilibrium  with  an  example. 


EQUILIBRIUM  OF  TTEAT  AND  COLD.  39 

and,  in  such  a case,  fall  in  the  shape  of  sleet,  which  is  half- 
melted  snow  or  hail. 

EQUILIBRIUM  OF  HEAT  AND  COLD. 

110.  Heat  has  a constant  tendency  to  preserve  an  equili- 
brium in  all  situations  ; and  hence  its  diffusion  through 
nature,  and  many  of  the  ordinary  phenomena  in  relation  to 
temperature.  When  we  touch  a cold  substance  with  our 
hand,  a portion  of  the  heat  of  the  hand  rushes  into  the 
substance,  and  leaves  the  hand  so  much  deficient  of  its 
former  heat.  On  the  same  principle,  when  we  touch  a 
substance  which  is  warmer  than  the  hand,  some  of  the  heat 
rushes  into  the  hand,  and  renders  it  hot.  When  we  pour 
a quantity  of  hot  water  into  that  which  is  cold,  an  equal- 
ization of  the  two  temperatures  immediately  ensues.  When 
the  air  at  any  particular  place  becomes  heated  or  rarified, 
it  ascends  by  virtue  of  its  greater  lightness,  leaving  a 
vacancy  which  the  neighbouring  air  rushes  in  to  supply. 
This  is  one  of  the  chief  causes  of  winds.  The  same  prin- 
ciple is  observable  in  the  case  of  heated  apartments.  If 
the  door  of  a heated  room  be  thrown  open,  a current  of 
cold  air  immediately  rushes  in  to  supply  the  deficiency  in 
the  rarified  atmosphere. 

111.  Evaporation  is  always  accompanied  by  the  with- 
drawal of  heat,  or  production  of  cold,  when  no  heat  is 
directly  applied  ; the  heat  necessary  for  the  production 
of  the  vapour  is  then  derived  or  radiated  from  surround- 
ing objects,  as  is  mentioned  above  in  the  case  of  dew  form- 
ing on  plants. 

1 12.  Examples  of  spontaneous  evaporation  producing 
cold,  are  familiar  to  most  persons.  Bathe  the  temples 
with  spirits,  and  the  quick  evaporation  of  the  fluid  will 
produce  a feeling  of  considerable  cold.  A current  of  air, 
when  not  loaded  with  moisture,  promotes  evaporation ; 
hence  the  rapidity  with  which  a wet  surface  generally 
dries  on  a windy  day. 


101.  How  does  this  explain  winds  ? 

102.  What  of  evaporation,  and  how  illustrated  ? 


40 


ARTIFICIAL  FREEZING TEMPERATURE. 


ARTIFICIAL  FREEZING  APPARATUS. 

113.  The  circumstance  of  evaporation  absorbing  heat, 
and  so  producing  cold,  has  led  to  the  discovery  of  a plan 
by  which  water  may  be  frozen  into  ice  by  simple  artificial 
means,  even  in  a warm  room.  The  apparatus  for  per- 
forming the  operation  consists  of  an  air-pump  and  its  re- 
ceiver. The  receiver  is  a spacious  glass  vessel  standing 
with  its  open  end  downwards  on  a flat  dish,  and  which 
can  be  exhausted  of  air  by  the  pump.  In  the  dish  a 
quantity  of  sulphuric  acid  is  placed,  and  in  the  centre  of 
the  dish  stands  a cup  or  a tripod  holding  some  water. 
The  air  being  pumped  from  the  receiver,  the  atmospheric 
pressure  is  removed  from  the  water  ; evaporation  rapidly 
ensues  ; the  vapour  as  it  rises  is  absorbed  by  the  sulphuric 
acid,  by  which  a vacuum  is  kept  up  ; the  temperature  of 
the  water  sinks  to  the  freezing  point,  and  soon  exhibits  a 
cake  -or  mass  of  ice.  A powerful  air-pump  operating  on 
several  receivers  will  produce  six  pounds  of  ice  in  about 
an  hour.  Instead  of  sulphuric  acid,  highly  toasted  and 
dried  oatmeal  will  answer  the  purpose  of  absorption. 

GRADUAL  ALTERATION  OF  TEMPERATURE. 

114.  In  the  great  operations  of  nature,  the  withdrawal 
of  heat  to  produce  intense  cold,  and  the  application  of  heat 
to  produce  great  warmth,  ordinarily  take  place  gradually. 
Thus,  although  water  freezes  at  a temperature  of  32,  it  is 
some  time  before  frost  is  completely  effectual  in  changing 
the  aspect  and  condition  of  liquid  bodies ; and  when  the 
temperature  rises  a few.  degrees  above  32,  after  a frost, 
the  ice  and  snow  which  have  been  formed  do  not  vanish 
immediately  ; indeed,  ice  will  remain  unthawed  for  several 
days  after  the  temperature  has  risen  some  degrees  above 
the  freezing  point.  By  this  slow  process,  either  in  the 
absorption  or  evolution  of  heat,  the  animal  and  vegetable 
worlds  are  not  liable  to  the  injury  which  would  ensue 


103.  How  is  artificial  freezing  explained  i 

104.  What  of  changes  of  temperature  ? 


EXPANSION  IN  COOLING DENSITY  IN  WATER.  41 

from  instantaneous  changes  in  the  condition  of  their  ele- 
mentary fluids. 

EXPANSION  IN  COOLING CRYSTALLIZATION. 

115.  It  has  been  observed  that  heat  expands  most  bodies 
in  proportion  as  it  is  increased  in  quantity.  There  are 
also  instances  in  which  substances  expand  in  cooling  as 
well  as  in  heating.  These  substances  are  water,  iron, 
antimony,  bismuth,  and  many  salts,  in  which  solidification 
takes  place  by  crystallization.  In  the  cooling  of  melted 
lead,  gold,  or  silver,  the  atoms  solidify  into  a dense  com- 
pact mass,  leaving  no  visible  pores  between  them.  But 
when  the  atoms  of  water,  melted  iron,  and  other  sub- 
stances, solidify,  they  arrange  themselves  in  the  form  of 
crystals,  or  minute  needle-like  parts  shooting  out  in  all 
directions,  and  leaving  pores  or  vacant  spaces  in  the  mass. 
Thus,  by  the  incorporation  of  pores,  the  bulk  of  the  body 
is  increased.  Crystallization  produces  beautiful  and 
regularly  formed  bodies,  the  forms  being  obviously  the 
result  of  certain  fixed  laws,  which,  however,  are  not  yet 
very  well  defined  or  understood. 

POINT  OF  GREATEST  DENSITY  IN  WATER. 

116.  The  point  of  temperature  at  which  water  is  most 
dense,  is  46  degrees  (or,  according  to  some  authors,  39|). 
When  the  temperature  is  reduced  below  this  point,  the 
volume  increases  till  it  reach  32,  when  the  liquid  freezes. 
When  the  temperature  is  raised  above  40,  the  voiume 
increases  till  it  reach  the  boiling  point.  Therefore,  at  any 
temperature  below  40,  as  at  35,  its  volume  is  the  same 
as  for  a temperature  as  many  degrees  above  40,  that  is, 
at  45. 

117.  When  the  surface  of  a body  of  water,  whose 
temperature  exceeds  46,  is  exposed  to  a lower  tempera- 
ture, the  water  at  the  surface,  when  it  is  reduced  in  the 
least  degree,  becomes  heavier  than  the  water  beneath,  and 


10e.  What  substances  expand  on  cooling? 

10n.  What  differences  in  the  solidification  of  bodies  ? 

107.  How  does  certain  temperature  affect  the  density  of  water? 


42 


EFFECTS  OF  FROST. 


it  consequently  descends,  its  place  being  now  occupied  by 
a stratum  of  higher  temperature,  which  is  n >xt  cooled  down 
and  descends  like  the  former ; and  this  process  continues 
till  the  temperature  of  the  whole  mass  is  reduced  to  40 
degrees.  After  the  temperature  has  reached  this  point, 
the  water  at  the  surface  becomes  lighter  than  the  sub- 
jacent mass,  and  it  consequently  remains  stationary.  If 
the  temperature  be  lowered  to  or  below  32,  congelation 
takes  place  ; and  as  ice,  from  its  porosity,  is  lighter  than 
water,  it  floats  on  the  surface.  From  this  circumstance, 
the  process  of  congelation  is  retarded  ; for  the  latent  heat 
or  caloric  of  the  water,  which  is  in  contact  with  the  lower 
surface  of  the  ice,  evolved  during  congelation,  instead  of 
being  quickly  carried  off  by  the  atmosphere,  as  it  would 
be  were  there  no  ice  over  it,  must  pass  through  the  ice, 
which  is  a bad  conductor  of  heat ; and  this  circumstance 
consequently  causes  a delay  in  the  process  of  congelation. 
Were  it  not  for  this  evolution  of  latent  caloric  during  con- 
gelation, and  the  buoyancy  of  ice,  rivers  would  frequently 
be  converted  into  one  solid  mass. 

EFFECTS  OF  FROST. 

118.  The  circumstance  of  water  being  increased  in 
volume  by  congelation,  explains  the  ordinary  phenomenon 
of  the  bursting  of  water-pipes,  and  other  similar  occur- 
rences, during  frost.  When  a vessel  of  moderate  strength 
is  filled  with  water,  its  expansion,  when  it  is  converted 
into  ice,  by  exposure  to  a freezing  temperature,  causes 
the  vessel  to  burst.  If  the  vessel  is  not  brittle,  but  pos- 
sessed of  considerable  tenacity,  as  a leaden  water-pipe, 
the  rupture  will  seldom  be  observed  during  the  continu- 
ance of  the  frost  while  the  water  remains  in  a solid  state, 
but  it  readily  appears  when  thaw  takes  place,  as  the  water 
is  then  forced  out  with  a velocity  corresponding  to  the 
vertical  height  of  the  column  of  water  in  the  pipe.  The 


108.  Explain  the  phenomenon  of  freezing  water. 

109.  What  explains  the  buoyancy  of  ice  ? 

110.  What  becomes  of  the  latent  heat  ? 

111.  Illustrate  the  expansion  of  water  by  freezing. 


EFFECTS  OF  FROST. 


43 


fissures  of  rocks,  too,  are  widened  by  the  freezing  of  the 
water  which  may  happen  to  lodge  in  them  before  frost ; 
and  this  process,  therefore,  is  a powerful  agent  in  the 
disintegration  of  rocks.  Portions  of  steep  banks,  also, 
from  a similar  cause,  tumble  down  after  thaw;  for  the 
moisture  in  them  expands  when  frozen,  and  thus  rends 
them  to  pieces,  which,  however,  during  the  frost,  are 
bound  together  as  by  cement,  and  fall  down  whenever 
thaw  dissolves  the  moisture.  On  the  same  principle  may 
be  explained  the  mouldering  of  soils  which  are  turned 
over  and  exposed  to  the  winter  frosts.  The  moisture  in 
the  soil  is  frozen,  which  rends  it  into  minute  portions, 
which  remain  firmly  united  during  frost,  but  crumble 
down  whenever  thaw  takes  place.  It  may  also  be  fre- 
quently observed,  that  footpaths,  especially  when  com- 
posed of  a mixture  of  earth  and  gravel,  are  considerably 
raised  during  frost  by  the  expansion  of  the  frozen  mois- 
ture in  them,  and  they  consequently  become  very  soft 
after  thaw.  The  husbandman  is  well  acquainted  with 
these  effects,  and  takes  advantage  of  them  by  turning  up 
the  soil,  and  thus  exposing  it  to  the  influence  of  the  winter 
frosts,  which  easily  produce  effects  that  w'ould  otherwise 
require  a great  amount  of  mechanical  labour,  skilfully  ap- 
plied, to  accomplish. 

119.  To  prove  that  water  expands  in  freezing,  place  a 
phial  full  of  water,  and  well  corked,  in  a situation  exposed 
to  frost.  In  a short  time  the  phial  will  be  observed  to  be 
cracked  all  over  by  the  expansion.  If  the  cork  be  left 
out,  it  will  be  observed  that  an  expansion  has  taken  place 
upwards,  and  a mass  of  ice,  resembling  a cork  in  figure, 
has  been  projected  above  the  mouth  of  the  phial. 

120.  As  ice  thaws,  it  gives  forth  the  air  which  it  had 
incorporated  in  its  pores  ; and  this  air,  being  of  a highei 
temperature  than  the  surrounding  water,  buoys  up  bubbles 
or  air  globules  on  the  surface.  Hence  the  froth  on  the 
surface  and  margins  of  lately  frozen  brooks. 


112.  What  effects  upon  the  soil? 

113.  What  simple  experiment  is  cited  ? 

1 14.  Explain  the  results  of  a thaw. 


44 


SHRINKING  OF  BODIES  BY  HEAT. 


SHRINKING  OF  BODIES  BY  HEAT. 

121.  Heat  has  a powerful  effect  in  causing  certain 
bodies  to  shrink  and  diminish  in  volume.  This  happens 
with  those  substances  which  do  not  liquify,  such  as  wood 
and  clay.  The  contraction  arises  from  the  heat  carrying 
off  the  watery  particles  from  the  bodies,  and  thus  allowing 
the  constituent  atoms  to  come  more  closely  together.  As 
wood  becomes  drier,  its  fibres  are  sometimes  split  asunder, 
so  as  to  emit  loud  cracking  noises,  which,  in  the  case  of  _ 
household  furniture,  are  ascribed  by  the  ignorant  to  super- 
natural causes. 

IGNITION  OF  BODIES FIRE. 

122.  Most  bodies  which  are  not  convertible  into  vapour 
by  the  application  of  heat,  as  in  the  case  of  the  wood  just 
mentioned,  are  ignitible,  and  become  luminous  in  the  dark, 
when  heated  to  800  degrees,  or  about  1000  when  heated 
in  the  day-light.  This  is  observed  equally  in  combustible 
solids,  as  charcoal,  and  in  stony  or  other  matters  which  do 
not  flame.  Combustible  bodies,  when  in  the  state  of 
luminous  heat,  are  said  to  be  on  fire,  or  ignited. 

123.  From  a state  of  simple  ignition,  heat  may  be  aug- 
mented in  intensity  to  a very  high  degree,  till  it  exhibit, 
as  is  observable  in  furnaces,  a white  luminous  appearance, 
at  which  height  of  temperature  most  metals  and  other  sub- 
stances are  melted,  and,  if  not  removed  and  cooled,  they 
are  in  a certain  time  destroyed.  Fire  is  active  in  propor- 
tion to  the  combustibility  of  the  substances  on  which  it 
acts,  and  to  the  quantity  of  atmospheric  air  which  is 
afforded  to  it.  When  fire  is  deprived  of  air,  it  speedily 
ceases,  and  is  extinguished. 

124.  The  principal  effects  produced  by  heat  or  caloric 
have  now  been  mentioned  ; namely,  repulsion  of  atoms  or 
expansion,  liquefaction,  vaporization,  evaporation,  and  igni- 
tion ; also  the  effects  produced  by  its  withdrawal,  namely, 

115.  What  bodies  contract  by  heat,  and  why? 

1 16.  What  of  ignition,  and  at  what  temperature  ? 

1 17.  What  of  combustible  bodies  ? 


DENSITY  OF  WATER. 


45 


condensation,  cold,  freezing,  and  crystallization.  A further 
consideration  of  the  subject,  particularly  as  regards  com- 
bustion, belongs  to  Chemistry.  Under  the  beads  Pneu- 
matics and  Meteorology,  some  of  the  leading  properties 
of  heat  will  be  recurred  to,  in  connection  with  atmospheric 
phenomena. 

ACCIDENTAL  PROPERTIES  OF  MATTER. 

125.  While  the  beautiful  and  extensive  variety  of  form 
in  bodies — solid,  liquid,  gaseous  and  the  different  modifi- 
cations of  these — are  to  be  traced  to  the  operation  of  chiefly 
two  great  leading  principles  in  nature,  attraction  and  re- 
pulsion, the  peculiar  forms  or  characters  which  bodies 
assume  from  the  influence  of  these  or  other  causes,  are 
usually  described  as  the  accidental  properties  of 
matter,  for  they  depend  on  circumstances  and  are  sus- 
ceptible of  variation.  The  following  is  a summary  of 
these  accidental  properties  : — Density,  Porosity  or  Rari- 
ty, Compressibility,  Elasticity,  Dilatation,  Hardness, 
Brittleness,  Malleability,  Ductility,  and  Tenacity. 

DENSITY  OF  BODIES. 

126.  Density  signifies  closeness  of  texture,  or  com- 
pactness. Bodies  are  most  dense  when  in  the  solid  state, 
less  dense  when  in  the  condition  of  liquids,  and  least  dense 
of  all  when  gaseous  or  aeriform.  In  this  manner  the 
degree  of  density  is  in  agreement  with  the  closeness  of  the 
atoms  to  each  other.  The  density  of  bodies  may  generally 
be  altered  by  artificial  means,  as  is  afterwards  mentioned. 
The  metals,  in  particular,  may  have  the  quality  of  density 
increased  by  hammering,  by  which  their  pores  are  made 
smaller,  and  their  constituent  particles  are  brought  nearer 
to  each  other. 

127.  The  more  dense  in  substance  that  a body  is,  it  is 
the  more  heavy  or  weighty.  In  speaking  of  the  density 
of  different  solid  and  liquid  bodies,  the  term  specific  gravity 


118.  Name  the  accidenml  properties  of  matter. 

119.  Detine  density.  ..rid  its  peculiarities. 


4G  DENSITY SPECIFIC  GRAVITY  OF  LIQU' 

is  used  to  denote  the  comparison  wmcti  is  made.  Thus, 
the  specific  gravity  of  a lump  of  lead  is  greater  than  an 
equal  bulk  of  cork  ; or  the  specific  gravity  of  water  is  greater 
than  that  of  an  equal  quantity  of  spirituous  fluid.  For 
the  sake  of  convenience,  pure  distilled  water,  at  a tempera- 
ture of  62  degrees,  has  been  established  as  a standard  by 
which  to  compare  the  specific  gravity  or  relative  weights 
of  bodies.  Water,  as  the  standard,  is  thus  said  to  be  1. 
When,  therefore,  any  body,  bulk  for  bulk,  is  double  the 
specific  gravity  of  water,  it  is  called  2,  and  so  on  to  3 and 
4 times,  up  to  22  times,  which  is  the  specific  gravity  of 
platinum,  the  heaviest  known  substance.  In  almost  every 
case  of  comparison  there  are  fractional  parts,  and  these  are 
usually  written  in  figures,  according  to  the  following  ar- 
rangement : Fractional  parts  are  divided  into  tens,  hun- 
dreds, thousands,  and  so  on.  If,  in  addition,  to  the  figure 
expressing  the  main  part  of  the  specific  gravity,  there  be 
one  other  figure,  with  a dot  or  point  between  them — thus 
2-5 — the  additional  figure  signifies  tenths,  and  the  body  is 
two  times  and  five-tenths  parts  of  a time  more  dense  or 
heavy  than  water.  If  two  figures  occur — thus,  10-40 — 
hundredths  are  signified,  and  the  body  is  ten  times  and 
forty-hundredth  parts  of  a time  heavier  than  water.  If 
there  be  three  figures,  thousandths  of  parts  of  a time  are 
meant ; if  four  figures,  ten  thousandth  parts  ; and  so  on. 
Common  air  is  sometimes  taken  as  a standard  with  which 
to  compare  gases,  being  a more  simple  mode  of  comparing 
the  relative  weights  of  aerial  substances.  But  all  the 
solids  and  liquids  are  estimated  with  reference  to  water  as 
the  standard. 

128.  Any  body  of  greater  specific  gravity  than  water, 
will  sink  on  being  thrown  into  water  ; but  it  will  float  on 
the  surface,  if  its  specific  gravity  be  less  than  that  of 
water.  A body,  such  as  a piece  of  wood,  after  floating  a 
certain  length  of  time  on  water,  will  imbibe  such  a 
quantity  of  liquid  that  its  specific  gravity  will  be  gradually 


120.  What  is  specific  gravity  ? 

121.  How  is  this  quality  measured  ? 

122.  What  of  fractional  parts  > 

123.  By  what  standard  ate  gases  weighed  ? 


SPECIFIC  GRAVITY  OF  LIQUIDS. 


47 


increased,  and  in  the  coarse  of  time  it  may  sink  to  the 
bottom. 

129.  The  density  of  liquid  bodies  is  liable  to  be  altered 
by  intermixture ; for  an  increase  or  diminution  of  bulk 
often  attends  the  combination  of  two  different  ingredients. 
Thus,  a cubic  inch  of  alcohol,  a strong  spirituous  fluid, 
mixed  with  a cubic  inch  of  water,  will  produce  a measure 
less  than  two  cubic  inches  ; in  mixing  strong  spirits  with 
water,  a diminution  of  about  4 gallons  in  the  100  takes 
place.  The  diminution  in  all  such  cases  is  occasioned  by 
the  mutual  penetration  of  the  particles  of  spirits  and  water; 
each  liquid  fills  up  the  interstices  in  the  other.  An  ex- 
ample of  a combination  of  two  bodies  producing  a body 
larger  than  the  two  bodies  were  individually,  is  seen  in 
the  case  of  incorporating  tin  with  lead,  by  which  an  in- 
crease of  bulk  takes  place. 

130.  Water  is  of  a greater  density  or  specific  gravity 
than  spirits ; consequently,  spirits  are  apt  to  float  on  the 
surface  of  water,  unless  the  two  liquids  be  well  mixed,  so 
as  to  produce  a mutual  incorporation  of  parts.  A body 
which  will  float  on  water  may  sink  in  spirits.  Although 
water  has  thus  the  greatest  power  of  buoying  up,  it  is  in 
ordinary  language  called  weak  ; and  spirits,  the  lighter 
they  are,  are  called  the  more  strong.  A knowledge  of 
this  relative  power  of  buoying  up  has  led  to  methods  for 
discovering  the  strength  of  spirits.  Small  hollow  glass 
beads,  marked  of  different  weights,  are  thrown  into  spirits ; 
and  the  lighter,  that  is,  the  stronger,  the  fluid,  the  less 
weight  of  bead  will  be  sustained.  An  instrument,  con- 
sisting of  a loaded  hollow  brass  ball,  and  a rod  with  a 
graduated  scale  of  figures  rising  from  it,  called  a hi/dro- 
me'er,  answers  the  same  purpose.  The  ball,  on  being 
let  into  the  fluid,  sinks  in  proportion  to  the  lightness  of  the 
spirits,  and  the  degree  of  strength  is  indicated  by  the 
figure  to  which  the  liquid  rises  on  the  graduated  scale. 
There  is  a certain  point  of  strength  called  propf.  below 


124.  Wha  varieties  in  the  density  of  bodies  occur  on  mixture  ? 

125.  How  is  i he  strength  ot  spiri  s resied? 

126.  Describe  a hydrometer , and  its  use. 


48 


SPECIFIC  GRAVITY  OF  SOLIDS. 


which  all  liquids  of  a spirituous  nature  are  legally 
prohibited. 

131.  In  making  calculations  of  the  strength  and  specific 
gravity  of  spirits,  by  the  above  or  any  other  means,  atten- 
tion must  be  paid  to  the  degree  of  temperature  of  the  fluid. 
Heat  expands  the  liquor,  and  renders  it  lighter  ; all  spirits 
are  therefore  more  bulky,  in  proportion  to  their  weight,  in 
summer  than  in  winter,  and  also  apparently  stronger,  not 
really  so.  A cubic  inch  of  brandy  will  weigh  10  grains 
less  in  summer  than  in  winter;  and  what  measures  33 
gallons  of  spirits  in  summer,  will  measure  only  32  in 
winter.  Thus,  if  a person  purchase  spirits  in  winter,  by 
measure  only,  and  sejl  them  again  in  summer,  by  measure 
only,  he  will  profit  to  the  extent  of  one  gallon  in  32.  To 
effect  sales  of  spirits  on  a principle  of  fairness,  both  to 
buyer  and  seller,  the  fluid  must  not  only  be  measured,  but 
its  specific  gravity  established  in  connection  with  its  de- 
gree of  temperature.  The  standard  heat  of  water,  by 
which  the  specific  gravity  of  liquids  is  compared,  is,  as 
already  mentioned,  62  degrees,  being  the  medium  tempe- 
rature all  over  the  globe.  If,  therefore,  spirits  be  above 
62  in  temperature,  a corresponding  deduction  must  be 
made  from  their  estimated  and  apparent  strength. 

132.  The  relative  specific  gravity  of  solid  bodies  of 
precisely  the  same  volume,  is  simply  ascertained  by 
weighing  them  in  opposite  scales  of  a balance,  and  the 
heavier  of  the  two  is  the  more  dense,  or  has  the  greater 
specific  gravity.  This  process,  however,  will  not  deter- 
mine the  true  intrinsic  value  or  character  of  any  given 
substance.  For  instance,  if  a man  were  to  bring  a piece 
of  metal  to  a goldsmith  for  sale,  calling  it  a pound  of  gold, 
and  the  goldsmith  put  it  in  a balance  and  found  that  it 
really  weighed  a pound,  there  would  be  no  certainty  that 
the  mass  was  wholly  gold ; it  is  possible  that  a portion  of 
it  might  be  lead,  silver,  copper,  or  any  other  inferior  metal. 
How,  then,  should  this  difficulty  be  adjusted  ? All  such 
questions,  in  relation  to  the  specific  gravity  of  bodies,  are 

127.  What  of  proof  spirits  t 

128.  How  are  the  effects  of  temperature  manifest  ? 

129.  How  is  the  relat.ve  specific  gravity  of  bodies  tested! 


POROSITY COMPRESSIBILITY. 


49 


solved  by  having  recourse  to  the  hydrostatic  balance,  an 
instrument  which  acts  upon  a principle  discovered  by 
Archimedes,  an  ancient  philosopher.  The  principle  is, 
that  the  specific  gravity  of  any  solid  may  be  determined 
by  the  bulk  of  water  which  a similar  solid  of  the  same 
weight  displaces  when  plunged  into  it.  The  goldsmith 
above  mentioned,  by  knowing,  in  the  first  place,  how 
much  water  a pound  of  pure  gold  displaces,  would  try 
the  metal  brought  to  him  by  that  standard ; in  other 
words,  he  would  see  whether  it  displaced  the  quantity  of 
water  proper  for  a pound  of  gold  ; if  it  displaced  more 
than  what  was  proper,  then  it  contained  alio}7,  was  too 
bulky  for  a pound  weight,  and  would  be  rejected  accord- 
ingly- 

POROSITY. 

133.  Porosity  is  the  quality  opposite  to  density,  and 
means  that  the  substance  to  which  it  is  applied  is  porous; 
that  is,  full  of  small  pores  or  empty  spaces  between  the 
particles,  and  that  the  body  is  comparatively  light.  The 
instances  of  porosity  are  numerous  in  every  department  of 
the  material  world,  but  those  which  are  connected  with 
animal  and  vegetable  bodies  are  the  most  remarkable. 
Bone  is  a tissue  of  pores  or  cells,  and,  when  seen  through 
a microscope,  may  be  said  to  resemble  a honeycomb. 
Wood  is  also  a tissue  of  cells  or  tubes.  If  the  end  of  a 
cylinder  of  straight  wood  be  immersed  in  water,  whilst  the 
other  is  forcibly  blown  into,  the  air  will  be  found  to  pass 
through  the  pores  of  the  wood,  and  rise  in  bubbles  through 
the  water.  When  a gas  is  comparatively  light,  it  is  said 
to  be  rare,  or  to  possess  rarity. 

COMPRESSIBILITY. 

134.  By  compressibility  is  meant  that  quality  in  virtue 
of  which  a body  allows  its  volume  to  be  diminished, 
without  the  quantity  or  mass  of  matter  being  diminished. 
It  arises,  of  course,  from  the  the  constituent  particles  being 


130.  What  of  the  hydrostatic  balance  ? 

131.  Define  poros  ty  with  examples. 


50 


ELASTICITY. 


brought  nearer  to  each  other,  and  is  effected  in  various 
ways.  All  bodies  are  less  or  more  capable  of  being 
diminished  in  bulk,  which  is  a conclusive  proof  of  tneir 
porosity. 

135.  Liquids  are  less  easily  compressed  than  solid 
bodies ; nevertheless  they,  to  a small  extent,  yield,  and  go 
into  smaller  bulk  by  great  pressure.  The  water  at  the 
bottom  of  the  sea,  by  being  pressed  down  by  the  superin- 
cumbent water,  is  more  dense  or  compact  than  it  would 
be  at  the  surface. 

136.  Atmospheric  air  and  gases  are  much  more  easily 
compressed  than  liquids,  or  even  than  many  solids.  Air 
may  be  compressed  into  a hundredth  part  of  its  ordinary 
volume.  When  at  this  state  of  compression,  it  has  a great 
tendency  to  expand  and  burst  the  vessel  in  which  it  is 
confined.  This  is  exemplified  in  the  air-gun,  in  which  a 
hundred  pints  of  air  are  pressed  into  the  size  of  one  pint ; 
and  it  is  the  force  with  which  the  confined  and  compressed 
air  hastens  to  resume  its  former  bulk,  that  causes  the  shot 
to  be  projected.  When  air  is  compressed  to  a much 
greater  degree  than  the  hundredth  part  of  its  ordinary 
bulk,  the  particles  of  matter  of  which  it  is  composed  col- 
lapse, and  become  so  dense  as  to  form  a liquid  of  an  oily 
nature ; in  which  case,  as  in  all  other  instances  of  com- 
pression, the  heat  which  held  the  particles  in  suspension 
is  forced  out,  and  is  felt  to  give  warmth  to  the  instrument 
or  vessel  in  which  the  operation  takes  place. 

ELASTICITY. 

137.  Some  bodies  have  the  power  of  resuming  their 
former  volume  or  shape  when  the  force  which  diminished 
it  is  withdrawn.  This  quality  is  termed  elasticity.  Steel 
is  one  of  the  most  elastic  of  metallic  bodies,  but  its  elasti- 
city is  not  nearly  so  great  as  that  of  India-rubber,  which, 
though  twisted,  drawn  out,  or  compressed  in  d iff  rent 
ways,  always  resumes  its  original  form.  The  aeriform 

132.  What  of  compressibility,  and  i f univeis:  lity  ? 

133.  What  of  this  property  in  air.  a id  its  effec  » i 

134.  What  of  the  extreme  compression  of  air  1 

135.  Define  elasticity  with  examples. 


HARDNESS,  BRITTLENESS,  MALLEABILITY. 


51 


fluids,  such  as  atmospheric  air,  and  the  gases,  are  all  ex- 
ceedingly elastic  ; and  so  are  liquids,  such  as  water,  but 
to  a smaller  extent. 


DILAT  ABILITY. 

158.  Dilatability  is  that  quality  of  bodies  by  which 
they  are  enabled  to  be  expanded  or  enlarged  in  their  di- 
mensions, without  any  addition  being  made  to  their  sub- 
stance. 

HARDNESS. 

139.  Hardness  is  the  quality  which  is  the  opposite  of 
softness,  and  does  not  depend  so  much  on  the  density  of 
the  substance,  as  the  force  with  which  the  particles  of  a 
body  cohere,  or  keep  their  places.  For  instance,  glass  is 
less  dense  than  most  of  the  metals,  and  it  is  so  hard  that 
it  is  capable  of  scratching  them.  Some  of  the  metals  are 
capable  of  being  made  either  hard  or  soft.  Steel,  when 
heaLed  to  a white  heat,  and  then  suddenly  cooled,  as  by 
immersion  in  water,  becomes  harder  than  glass  ; and  when 
cooled  slowly,  it  becomes  soft  and  flexible. 

BRITTLENESS. 

140.  Brittleness  is  that  quality  by  which  bodies  are 
capable  of  being  easily  broken  into  irregular  fragments ; 
and  it  belongs  chiefly  to  hard  bodies.  Iron,  steel,  brass, 
and  copper,  when  heated  and  suddenly  cooled,  become 
brittle. 

MALLEABILITY. 

141.  Malleability  is  the  quality  by  which  bodies  are 
capable  of  being  extended  by  hammering.  Some  of  the 
malleable  metals  are  gold,  silver,  copper,  zinc  at  the  tem- 
perature of  boiling  water,  lead,  iron,  and  some  others. 
Some  of  the  metals  possess  the  opposite  quality  of  brittle- 


136.  Explain  dilatability. 

137.  Upon  what  does  hardness  depend  ? examples. 

138.  Explain  brittleness,  with  examples. 


52  SUMMARY  OF  PROPERTIES  IN  BODIES. 

ness.  Gold  is  the  most,  malleable  of  all  metals,  and  it 
may  be  hammered  so  thin  as  to  be  translucent,  or  perme- 
able to  light. 

DUCTILITY. 

142.  By  ductility  is  understood  that  property  by  which 
metals  may  be  drawn  into  wire.  The  most  malleable 
metals  are  not  the  most  ductile.  Tin  and  lead  may  be  rolled 
into  thin  leaves,  but  cannot  be  drawn  into  wire.  The 
most  ductile  metal  is  platina,  which  can  be  drawn  into 
Avire  as  fine  as  the  threads  of  a cobweb. 

TENACITY. 

143.  Tenacity  is  the  quality  by  which  bodies  are  not 
easily  torn  asunder.  Steel  is  the  most  tenacious  of  all 
substances  ; a wire  of  this  metal,  the  hundredth  of  an  inch 
in  diameter,  will  support  a weight  of  134  lbs. ; while  one 
of  the  same  size  of  platina  will  sustain  only  16  lbs.,  and 
one  of  lead  only  2 lbs. 


SUMMARY  OF  PROPERTIES. 

We  have  now  presented  a definition  of  all  the  proper- 
ties or  qualities  usually  ascribed  to  matter,  and,  for  the 
sake  of  fixing  them  in  the  mind  of  the  pupil,  we  shall 
here  shortly  recapitulate  them. 

144.  The  essential  properties  of  matter  are  Impenetra- 
bility, Extension.  Figure,  Divisibility,  Inertia,  and  Attrac- 
tion. Attraction  is  an  essential  property  only  when  un- 
der the  character  of  attraction  of  gravitation,  or  terrestrial 
attraction,  as  it  is  sometimes  called.  When  exhibited 
under  its  supposed  modifications  in  relation  to  cohesion, 
capillary  attraction,  chemistry,  magnetism,  and  electricity, 
it  is  not  an  essential,  but  an  accidental  property,  for  it  acts 
only  according  to  circumstances.  These  modifications 
may  be  shortly  styled  Accidental  Varieties  of  Attraction. 


139.  What  of  malleability  and  ductility  ? 

140.  What  of  tenacity,  with  an  example  ? 

141.  Recapitulate  the  summary. 


MOTION  AND  MATTER. 


53 


1 15.  The  repulsive  or  expansive  quality  in  matter  is 
termed  Heat,  or  Caloric. 

■ 14H.  The  accidental  properties  of  matter  are  Density, 
Porosity  or  Rarity,  Compressibility,  Elasticity,  Dilatation, 
Hardness,  Brittleness,  Malleability,  Ductility,  and  Tena- 
city. 

MOTION  AND  FORCES— GENERAL  EXPLANA- 
TIONS. 

147.  Motion  is  the  changing  of  place,  or  the  opposite 
of  rest. 

148.  Matter,  according  to  the  definitions  which  have 
been  given  of  its  properties,  is  substance  devoid  of  life 
and  volition,  and  which  is  perfectly  passive,  or  inert.  It 
has  been  described  as  possessing  the  property  of  inertia, 
and  in  this  respect  it  is  said  to  possess  an  unwillingness 
or  reluctance  to  move ; but  these  phrases  are  only  figura- 
tive, and  are  used  for  the  purpose  of  conveying  a forcible 
idea  of  the  passiveness  of  its  character.  It  is  also,  in 
consequence  of  this  property  of  inertia,  or  passiveness  to 
submit  to  any  condition  to  which  it  is  subjected,  that  a 
body,  when  once  in  motion,  will  continue  to  move  conti- 
nually with  the  same  velocity  and  in  the  same  direction, 
till  it  be  disturbed  by  some  external  cause. 

149.  Any  instance  of  rest  which  comes  under  our  ob- 
servation, is  only  rest  in  a relative , not  an  absolute,  sense  ; 
that  is,  it  is  rest  as  relates  to  the  earth,  but  not  rest  as  re- 
lates to  the  universe  ; for  though  the  stone  which  falls  to 
the  ground  lies  at  rest  on  the  earth,  the  earth  is  always  in 
motion,  and  therefore  the  stone  is  no  more  at  rest  than 
the  insect  which  sits  upon  a moving  wheel  is  at  rest. 
Hence,  in  speaking  of  bodies  coming  apparently  to  a state 
of  rest,  we  must  always  recollect,  that  it  is  only  relative, 
not  positive  or  absolute  rest.  It  is  supposed  that  there  is 
no  such  thing  as  absolute  rest  in  creation.  All  the  planets 


142.  Define  motion  and  matter. 

143.  What  is  ascribed  to  inertia  ? 

144.  What  is  said  of  absolute  rest  ? 


54 


MOTION  IN  MATTER. 


are  in  motion  round  the  sun  ; the  sun  itself  has  a motion 
on  its  own  axis  ; it  is  also  believed  by  many  astronomers 
that  the  sun  has  an  onward  or  progressive  motion  in 
space,  besides  its  rotary  movement ; and  thus,  perhaps, 
revolves  round  some  distant  centre,  with  all  its  planets  in 
its  train. 

150.  Common  experience  would  lead  to  the  conviction 
that  rest  is  more  natural  for  matter  than  motion  : but  this 
conviction  is  founded  on  a limited  consideration  of  circum- 
stances. The  reason  why  we  see  ordinary  moving  bodies 
coming  to  a state  of  rest — such  as  a wheel  stopping  after 
having  been  whirled  on  its  axle,  a ball  stopping  after  roll- 
ing on  the  ground,  or  an  object  falling  to  the  earth  after 
being  thrown  upwards — is,  that  they  are  sooner  or  later 
arrested  in  their  progress  by  the  earth’s  attraction  or  their 
own  gravity,  by  the  friction  or  rubbing  against  some  other 
body,  or  by  the  opposition  presented  to  them  by  the  at- 
mosphere. Except  for  these  three  pr  vailinc  causes  of 
impediment  and  stoppage,'  all  bodies  once  set  in  motion 
would  go  on  moving  for  ever.  Taking  this  expanded 
view  of  things,  and  dismissing  the  erroneous  impressions 
arising  from  what  is  obvious  only  to  pur  limited  experi- 
ence, we  find  that  there  is  nothing  more  remarkable  in 
perpetual  motion  than  in  perpetual  rest. 

151.  It  is  only,  however,  in  the  great  works  of  creation, 
or  the  heavenly  bodies,  that  perpetual  motion  is  observ- 
able. The  planetary  bodies  are  under  the  ever-acting 
impulses  of  centrifugal  and  centripetal  forces,  and  are  not 
impeded  by  friction,  or  by  the  atmosphere,  for  they  move 
in  space,  or  in  a comparative  vacuum.  Many  ingenious 
attempts  have  bi  en  made  to  produce  perpetual  motion  on 
mechanical  principles  in  terrestrial  objects,  but  they  have 
all  necessarily  failed,  as  no  human  effort  can  destroy  gravity 
in  bodies,  or  altogether  prevent  friction  in  movement. 

152.  In  regard  to  bodies  on  the  earth,  of  which  a state 


145.  Why  does  rest  seem  to  be  the  natural  state  of  matter  ? 

146.  What  agencies  obstruct  motion? 

147.  What  examples  have  we  of  perpetual  motion? 

148.  Why  have  all  experiments  failed  to  discover  perpetual  motion 
in  machinery  ? 


FORCES  OR  TOWERS. 


55 


of  rest  is  the  ordinary  condition,  motion  is  produced  by 
ceriain  agencies,  or  impelling  causes,  either  belonging  to 
the  phenomena  of  nature  or  to  art.  The  property  of  ca- 
pillary attraction  causes  a motion  in  liquids  under  certain 
circumstances;  the  winds  blow, and  cause  motion;  rivers, 
in  flowing  down  their  channels,  and  the  action  of  the  tides, 
likewise  produce  motion ; thus,  there  exist  many  natural 
causes  of  motion,  which  are  taken  advantage  of  by  man 
in  the  economy  of  arts  and  manufactures.  Motion  in  the 
animal  economy  is  produced  by  a principle  of  life  ; but 
of  the  nature  of  this  kind  of  motion  mankind  are  ignorant, 
and  nothing  here  requires  to  be  said  regarding  it.  The 
causes  of  motion  which  have  to  engage  our  attention  are 
those  which  consist  o i forces,  whether  natural  or  artificial, 
and  which  forces  have  the  property  of  impelling  inani- 
mate objects  from  a state  of  rest  to  a state  of  motion,  of 
stopping  them  when  in  motion,  or  of  altering  the  character 
of  their  motion.  These  forces  are  also  called  powers. 

153.  Motion,  according  to  the  mode  in  which  the  force 
acts,  is  susceptible  of  innumerable  variations.  According 
as  the  moving  body  is  affected,  it  may  move  rapidly  or 
slowly  ; proceed  in  a straight  line,  turn  in  a circle  or 
curve  ; it  may  move  with  uniform  or  irregular  speed,  or 
be  retarded  or  accelerated.  The  body  may  also  move 
upon  or  in  respect  of  another  body  which  is  also  moving. 
Some  of  these  peculiarities  in  motion  will  immediately 
engage  our  attention  ; meanwhile.  it  has  to  be  explained, 
that,  for  the  sake  of  convenience  in  language,  and  accu- 
racy in  the  application  of  terms,  certain  words  are  used 
to  define  the  nature  of  motion  in  bodies,  and  the  forces 
affecting  them. 

154.  Motion  is  said  to  be  common  to  two  or  more  bodies 
when  they  move  in  contact  or  together ; or  when,  though 
not  in  contact,  they  are  carried  along  in  a similar  manner, 
and  with  the  same  velocity  ; that  is,  when  they  have  a 
motion  in  common,  or  participate  in  the  same  motion. 
Motion  is  said  to  be  absolute, w hen  a body  actually  moves 

149.  What  phenomena  of  motion  are  produced  in  nature? 

150.  What  of  the  varieties  of  motion  ? 

151.  Define  common  motion. 


MOMENTUM. 


56 

from  one  point  of  space  to  another,  or  when  it  moves  to- 
wards, or  when  it  passes,  another  which  is  at  rest.  There- 
fore, setting  aside  the  idea  of  the  earth  moving,  we  should 
say  that  a vessel  moving  on  the  sea  has  an  absolute  mo- 
tion, while  the  land  is  fixed  or  stationary.  Motion  is  said 
to  be  relative-,  when  the  motion  of  one  moving  body  is 
considered  in  reference  to  that  of  another  movjng  body. 
Thus,  if  two  bodies  move  in  the  same  direction,  their  rela- 
tive motion  is  the  difference  of  their  motions  ; if  they 
move  in  opposite  directions,  it  is  the  sum  of  their  separate 
motions. 

155.  When  a force,  applied  to  any  material  object,  is 
resisted  or  counteracted,  so  that  no  motion  ensues,  it  is 
called  a pressure  ; and  forces  so  counteracted  are  said  to 
balance  each  other,  or  to  be  in  equilibrium. 

156.  The  degree  of  speed  in  the  motion  of  bodies  is 
called  velocity.  Velocity  is  measured  by  the  space  or 
distance  passed  over,  with  an  invariable  motion,  and  in  a 
given  time,  as  one  second.  Thus,  if  a body,  in  one  second, 
with  an  invariable  motion,  pass  over  twenty  feet,  its  velo- 
city is  said  to  be  twenty  feet  per  second. 

157.  When  a motion  is  invariable,  it  is  said  to  he  uni- 
form ; if  it  be  gradually  increasing,  it  is  said  to  he  accel- 
erated ; and  if  it  gradually  decrease,  it  is  said  to  be  re- 
tarded. A force  is  said  to  be  an  accelerating  or  retarding 
force,  according  as  it  produces  an  accelerated  or  retarded 
motion. 

15b.  Forces  are  either  instantaneous  or  continued.  The 
former  is  an  impulse,  like  a stroke  ; the  latter  acts  without 
intermission.  When  a continued  force  remains  always 
of  the  same  intensity,  it  is  called  a constant  force.  Other 
continued  forces  are  said  to  be  variable. 

159.  A body,  in  moving,  possesses  a force  which  is 
called  its  momentum,  or  motal force.  Momentum  is  very 
different  from  velocity.  A light  body  and  a heavy  body 
may  move  at  the  same  velocity,  but  the  momentum  of  the 
light  body  will  be  small  in  comparison  with  that  of  the 

152.  Define  relative  and  absolute  motion. 

153.  Define  pressure,  balance,  velocity,  &e. 

J54.  Name  varieties  in  velocity  ? 


PHENOMENA  OF  FALLING  BODIES. 


57 


heavy  one.  The  light  one,  on  coming  to  a state  of  rest, 
will  perhaps  fall  harmlessly  on  the  ground,  while  the 
other,  by  its  momentum,  will  strike  forcibly  on  the  earth, 
or  destroy  any  object  which  opposes  it.  Momentum  is 
proportionate  to  the  mass  and  velocity  of  bodies,  and,  by 
multiplying  the  weight  by  the  number  of  feet  moved  over 
per  second,  we  find  that  the  momentum  is  the  product. 
Thus,  if  a body  of  twelve  ounces  move  with  a velocity  of 
twenty  feet  per  second,  its  momentum  is  (twelve  times 
twenty)  two  hundred  and  forty.  In  ordinary  language, 
the  term  impetus  is  used  to  signify  the  violent  tendency 
of  a moving  body  to  any  point. 

Before  entering  upon  a consideration  of  motion  as  pro- 
duced by  ordinary  forces,  it  will  be  appropriate  to  describe 
the  effects  produced  upon  bodies  when  simply  falling — 
that  is,  moving  downwards  towards  the  earth,  when  the 
supports  which  upheld  them  are  withdrawn. 

THE  PHENOMENA  OF  FALLING  BODIES— WEIGHT. 

160.  Attraction,  as  already  explained,  is  a force  inherent 
in  nature,  by  which  particles  and  masses  of  matter  are 
drawn  towards  each  other.  This  force,  it  has  also  been 
stated,  increases  in  proportion  to  the  quantity  of  matter 
which  the  attracting  body  contains,  and  it  also  increases  as 
th’e^bodies  approach  each  other. 

161.  Further,  it  has  been  mentioned  that  this  powerful 
and  subtile  quality  in  matter  is  the  cause  of  the  falling  or 
drawing  of  bodies  downwards  towards  the  earth,  and  thus 
produces  what  is  termed  weight  or  gravity.  Gravity, 
then,  is  simply  the  tendency  which  any  substance  has  to 
press  downwards  in  obedience  to  the  law  of  attraction,  as 
exemplified  in  the  phenomena  of  bodies  failing  from 
heights  to  the  ground,  when  the  supports  which  upheld 
them  are  removed. 

162.  All  falling  bodies  tend  directly  towards  the  centre 
of  the  earth,  in  a straight  line  from  the  point  where  they 
are  let  fall.  If,  then,  a body  be'let  fall  in  any  part  of  the 


155.  What  of  momentum  ? 

156.  Define  gravity,  and  illustrate. 


58 


PHENOMENA  OF  FALLING  BODIES. 


world,  the  line  of  its  direction  will  be  perpendicular  to  the 
earth’s  centre.  Consequently,  two  bodies  falling  on  op- 
posite sides  of  the  earth,  fall  towards  each  other. 

164.  Suppose  any  h dy  to  be  disengaged  from  a height 
opposite  to  us,  on  the  other  side  of  the  earth,  its  motion 
in  respect  to  us  would  be  upward,  while  the  downward 
motion  from  where  we  stand,  would  be  upward,  in  respect 
to  those  who  stand  opposite  to  us,  on  the  other  side  of  the 
earth. 

104.  In  like  manner,  if  the  falling  body  be  a quarter, 
instead  of  half  the  distance  round  the  earth  from  us,  its 
line  of  direction  would  be  directly  across,  or  sidewise, 
that  is,  at  right  angles  with  the  lines  already  supposed. 

165.  It  will  be  obvious,  therefore,  that  what  we  call  up 
and  down  are  merely  relative  terms,  and  that  what  is  down 
in  respect  to  us,  is  up  in  respect  to  those  who  live  on  the 
opposite  side  of  the  globe.  Consequently,  down  every- 
where means  towards  the  centre  of  the  earth,  and  up  sig- 
nifies from  the  centre  of  the  earth. 

166.  The  velocity  or  rapidity  of  every  falling  body  is 
uniformly  accelerated,  or  increased,  in  its  approach  towards 
the  earth,  from  whatever  height  it  falls,  if  the  resistance 
of  the  atmosphere  be  not  reckoned. 

167.  If  a rock  be  rolled  from  the  summit  of  a steep 
mountain,  its  motion  is  at  first  slow  and  gentle,  but .^s  it 
proceeds  downwards,  it  moves  with  perpetually  increased 
velocity,  seeming  to  gather  fresn  speed  every  moment, 
until  its  force  is  such  that  every  obstacle  is  overcome; 
trees  and  rocks  are  dashed  from  its  path,  and  its  motion 
does  not  cease  until  it  has  rolled  to  a great  distance  on  the 
plain. 

148.  The  same  principle  of  increased  velocity  in  bodies, 
as  they  descend  from  a height,  is  illustrated  by  pouring 
treacle,  honey,  or  any  thick  syrup,  from  an  elevated  ves- 
sel. The  bulky  stream,  which  is  perhaps  two  inches  in 
diameter  where  it  leaves  the  vessel,  is  reduced  to  the  size 
of  a straw  or  a thread  on  reaching  its  destination ; but 

157.  What  of  the  antipodes,  and  other  positions  ! 

158.  How  are  we  to  unders  and  down  and  up  > 

159.  How  is  momentum  and  velocity  increased, and  why  ? 


VELOCITY  OF  FALLING  BODIES. 


59 


what  it  wants  in  bulk  is  made  up  in  velocity,  for  the  small 
thread-like  stream  at  the  bottom  will  fill  a vessel  just  as 
soon  as  the  large  and  slow  moving  stream  at  the  outlet ; the 
velocity  is  indeed  so  great,  that  the  stream  has  not  time  to 
sink  at  once  into  the  mass  below,  but  falls  in  overlaying 
folds. 

1(59.  From  the  same  principle,  a person  may  leap 
from  a chair  without  danger;  but  if  he  jump  from  the 
house-top,  his  velocity  becomes  so  much  increased,  be- 
fore he  reaches  the  ground,  as  to  endanger  his  life  by  the 
fall. 

170.  It  is  found  by  experiment,  that  the  motion  of  a fall- 
ing body  is  increased,  or  accelerated,  in  regular  arithmetical 
progression.  In  other  words,  in  every  second  of  time  during 
its  descent,  it  acquires  an  additional  rate  of  speed,  the  rate 
regularly  increasing  by  the  accumulation  of  the  preceding 
additions. 

171.  It  is  ascertained  that  a dense  or  compact  body,  wh en 
fallingfreely,passesthroughaspace  of  10  feet  1 inch  during 
the  first  second  of  time.  Leaving  out  the  odd  inch  for  the 
sake  of  even  numbers,  we  find  that  the  space  fallen  through 
in  a given  time  is  determined  by  the  following  arithmetical 
computation. 

173.  Ascertain  the  number  of  seconds  which  a body  oc- 
cupies in  falling.  Take  the  square  of  that  number  (that  is, 
the  number  multiplied  by  itself),  and  multiply  the  square 
by  Id,  which  is  the  number  of  feet  fallen  during  the  first 
second,  and  the  result  is  the  amount  of  feet  which  the  body 
altogether  falls.  For  example,  if  a ball  occupy  3 seconds 
in  falling,  we  take  the  square  of  3,  which  is  9 ; then  we 
multiply  9 by  Id,  which  gives  144  as  the  result,  and  that 
is  the  number  of  feet  fallen.  Again,  if  we  find  that  the  ball 
occupy  4 seconds  in  falling,  we  take  the  square  of  4,  which 
is  Id,  and  multiply  16  by  1 0,  the  result  is  256,  which  is  the 
number  of  feet  fallen.  And  so  on,  always  following  the  same 
rule  of  computation. 


1G0.  What  examples  are  given  ? 

16],  In  what  proportion  does  velocity  increase  ? 
162.  Give  examples  of  the  calculation 


VELOCITY  O'  FALLING  BODIES. 


CO 


17.3.  It  is  not  always  easy,  by  the  above  mode  of  calcu- 
lation, to  arrive  at  a correct  result  as  to  the  height  fallen  by 
bodies,  and  all  that  can  be  expected  is  an  approximation 
to  a true  result.  This  arises  from  bodies  being  of  different 
bulks,  and  receiving  different  degrees  of  opposition  from 
the  atmosphere  in  their  descent.  It  is  a common  suppo- 
sition that  large  and  heavy  bodies  fall  more  quickly  than 
small  and  light  ones.  This  opinion,  which  was  maintained 
even  by  philosophers,  until  Galileo  rectified  the  mistake, 
perhaps  originates  in  the  error  of  confounding  momentum 
with  velocity.  Be  this  as  it  may,  it  is  now  an  ascertained 
truth  in  science,  that  all  bodies,  of  whatever  density,  fall 
with  the  same  velocity.  Thus,  a ball  containing  a pound 
of  lead  falls  with  the  same  velocity  as  a bail  containing  an 
ounce.  This  equality  in  the  rate  of  falling  is,  however, 
disturbed  by  the  quality  of  figure  and  bulk  of  bodies.  A 
solid  ball  of  gold  will  fall  more  quickly  than  the  same  quan- 
tity of  gold  beat  out  into  a thin  leaf,  because  in  the  case  of 
the  leaf  the  resistance  from  the  atmosphere  on  a large 
surface  impedes  the  descent.  Thus  the  atmosphere  pre- 
vents bulky  and  porous  substances  from  falling  with  the 
same  velocity  as  those  which  are  compact. 

174.  If  the  atmosphere  were  removed,  all  bodies,  whether 
light  or  heavy,  large  or  small,  would  descend  with  the  same 
velocity.  This  fact  is  ascertained  by  experiments  performed 
with  the  air-pump. 

1 15.  When  a piece  of  coin,  for  instance  a guinea,  and 
a feather,  are  let  fall  at  the  same  instant  of  time,  from  a 
hook  which  has  held  them  at  the  top  of  the  exhausted  re- 
ceiver of  an  air-pump,  they  are  observed  to  fall  at  an  equal 
rate,  and  to  strike  the  bottom  at  the  same  moment.  Hence 
it  is  demonstrated,  that  were  it  not  for  the  resistance  of  the 
atmosphere,  a bag  full  of  feathers,  and  one  of  coins,  would 
fall  from  a given  height  with  the  same  velocity,  and  in  the 
same  space  of  time. 

1/6.  It  has  been  stated  that  the  attraction  of  gravitation 

163.  What  mistake  results  from  confounding  momentum  with  ve- 
locity? 

164.  How  is  it  affected  by  bulk  and  figure,  and  why  ? 

165.  What  of  the  air-pump  ? 


THE  CENTRE  OF  GRAVITY. 


61 


increases  in  proportion  to  the  quantity  of  matter  which  the 
attracting  body  contains.  Thus,  the  mass  of  our  planet, 
the  earth,  exerts  a force  of  attraction  which  produces  the 
phenomena  of  weight,  and  the  falling  of  bodies  with  a cer- 
tain velocity. 

177.  In  consequence  of  the  different  size  and  density 
of  the  sun  and  planetary  bodies,  attraction  is  much  stronger  • 
in  some  of  them  than  others,  and  consequently  the  weight 
of  bodies  differs  in  each.  On  the  surface  of  the  sun,  our 
pound  weight  would  weigh  upwards  of  27  pounds,  and  a 
body  would  fall  upon  it  434  feet  the  first  second.  On  the 
surface  of  Jupiter,  our  pound  would  weigh  about  2 pounds 
4 ounces.  And  on  the  surface  of  the  moon,  our  pound 
would  weigh  only  the  fifth  part  of  a pound. 

178.  As  a body  in  descending  to  the  earth  receives  in- 
creasing accessions  to  its  velocity  during  every  successive 
second,  so  when  a body  is  projected  upwards  from  the 
surface  of  the  earth,  its  velocity  decreases  in  the  same  pro- 
portion, till  it  comes  to  a state  of  momentary  rest,  when  it 
instantly  begins  to  descend  with  a gradually  increasing 
velocity,  which  at  any  point  in  the  descent  is  equal  to  its 
velocity  at  the  same  point  when  ascending.  In  this  cal- 
culation, however  we  omit  the  influence  of  the  atmosphere, 
which  would  cause  the  final  velocity  in  the  descent  to  be 
less  than  the  original  velocity  with  which  the  body  was 
projected  upwards. 


THE  CENTRE  OF  GRAVITY. 

179.  Terrestrial  gravitation,  as  already  explained,  does 
not  act  on  the  mere  surface  of  bodies,  or  according  to  their 
bulk,  but  is  exerted  in  reference  to  all  the  particles  or 
atoms  individually  which  compose  the  mass  of  a body. 
As  the  earth  is  nearly  of  a spherical  form,  its  attraction  is 
the  same  nearly  as  if  it  proceeded  entirely  from  the  centre. 
On  account  of  the  great  size  of  the  earth,  compared  with 
that  of  any  ordinary  body  at  its  surface,  its  attractive  force 

166.  How  is  gravitation  increased  by  quantity  of  matter? 

167.  What  of  weight  on  the  different  planets  ? 

168.  What  of  the  velocity  of  bodies  thrown  upward  ? 


62  CENTRE  OF  GRAVITY. 

acts  in  straight  lines,  sensibly  parallel,  proceeding  from  the 
earth’s  centre.  In  the  case  of  liquids,  in  which  the  atoms 
slightly  cohere,  the  atoms  have  liberty  to  spread  them- 
selves over  the  earth,  and  to  seek  the  lowest  situation  for 
repose.  In  the  case  of  solids,  a different  operation  is  ob- 
servable. In  them,  the  particles  of  matter  stick  so  closely 
together,  that  they  are  not  at  liberty  to  obey  the  law  of 
gravitation  individually,  but  rally,  as  it  were,  round  a 
common  centre,  upon  which  the  force  of  attraction  may 
be  considered  to  act  for  the  general  behoof.  This  centre 
is  called  the  centre  of  gravity,  the  centre  of  inertia,  or 
the  centre  of  parallel  forces. 

180.  Every  solid  body  or  dense  mass  possesses  a centre 
of  gravity,  which  is  the  point  upon  or  about  which  the 
body  balances  itself,  and  remains  in  a state  of  rest,  or 
equilibrium,  in  any  position. 

181.  The  centre  of  gravity  may  be  described  as  a point 
in  solids  which  always  seeks  its  lowest  level,  in  the  same 
manner  that  the  lowest  level  is  sought  for  by  water ; for  it  is 
only  by  propping  up  the  body,  that  the  centre  of  gravity  is 
prevented  from  displaying  the  same  mode  of  action. 

182.  The  centre  of  gravity  in  round,  square,  or  other 
regular  shaped  bodies,  oh  uniform  density  in  ail  their 
parts,  is  the  centre  of  these  bodies. 

183.  When  a body  is  shaped  irregularly,  or  when  there 
are  two  or  more  bodies  connected,  the  centre  of  gravity  is 
the  point  about  which  they  will  balance  each  other. 

184.  Any  square  or  angular  body 
which  we  may  place  on  the  ground, 
will  remain  stationary,  or  safely  at 
rest,  provided  an  ideal  'ine,  drawn 
from  its  centre  of  gravity,  and  pass- 
ing to  the  ground  in  a direction  per- 
pendicular to  the  earth’s  surface,  fall 
within  its  base,  as  in  figure  1.  A 
point  below  A is  the  centre  of  gravity ; 
and  from  that  point  the  line  of  direc- 


Fig.  t. 


169.  What  is  meant  by  the  cenire  of  gravity,  & c.  ? 

170.  Describe  its  variation  in  different  bodies 


CENTRE  OF  GRAVITY. 


6-1 


lion  goes  downward  to  B,  which  is  within  the  edges  of  the 
base.  An  object  of  this  form,  and  so  placed,  will  stand. 

Fig.  2.  185.  If  the  line  of  direction  from 

the  centre  of  gravity  fall  without  the 
outer  edge  of  the  base,  as  in  figure  2, 
from  A to  B.  then  the  object  will  not 
remain  balanced  on  its  base  ; it  wi  i 
fall  over,  and  attain  some  position  in 
which  the  line  of  direction  falls  within 
the  boundary  of  the  base  on  which  it 
stands. 

188.  By  keeping  this  simple  prin- 
ciple in  view,  stability  and  safety  will  generally  be  secured 
m the  erection  of  objects  of  art.  such  as  houses,  monu- 
mental edifices,  spires,  and  obelisks,  as  well  as  in  the  lad- 
ing of  coaches,  carts,  and  other  vehicles,  and  the  piling 
of  timber  or  any  kind  of  goods  in  heaps.  In  every 
instance,  the  base  ought  to  be  sufficiently  broad  to  admit 
of  the  line  of  direction  from  the  centre  of  gravity  falling 
within  it. 

187.  A small  degree  of  experience -seems  to  point  out 
the  propriety  of  erecting  all  kinds  of  structures  with  a 
base  wide  enough  to  secure  stability  ; nevertheless,  in 
opposition  both  to  experience  and  the  simple  principles 
of  science,  we  often  find  that  stage-coaches  are  laden  in 
such  a manner  that  their  centre  of  gravity  is  liable  to  too 
great  a change  of  position,  and  that  they  are  overturned, 
to  the  personal  injury,  and  even  loss  of  life,  of  the  pas- 
sengers. The  error  in  these  instances  consists  in  raising 
the  centre  of  gravity  too  high.  At  first,  perhaps,  the 
centre  of  gravity  is  so  comparatively  low,  that,  in  the  case 
of  swaying  to  a side,  the  line  of  direction  would  fall  within 
the  edge  of  the  wheel,  and  no  danger  would  ensue  ; but  it 
is  common  to  go  on  piling  masses  of  goods  or  luggage,  or 
placing  a number  of  passengers,  on  the  roof  of  the  vehicle, 
so  that  the  centre  of  gravity  becomes  considerably  elevated ; 


171.  What  of  the  line  of  direction  ? 

172.  Wha:  practical  examples  are  cited  ? 

173.  Explain  the  upsetting  of  a vehicle. 


CENTRE  OF  CR  WTTY. 

F s ! so  high,  indeed,  that  when  the 

carriage  is  swayed  or  jolts  to 
one  side,  the  line  of  direction 
is  thrown  beyond  the  wheel, 
and  the  vehicle  will  conse- 
quently fall  over.  In  the  an- 
nexed cut,  figure  3,  a loaded 
vehicle  is  represented  cross- 
ing an  inclined  plane,  or  we 
may  suppose  that  its  wheel 
on  one  side  has  come  in  con- 
tact with  a stone  S.  which  has  raised  it  above  the  level  of 
the  other  wheel,  so  as  to  incline  the  body  of  the  vehicle 
very  considerably  from  the  horizontal.  The  centre  of 
gravity  is  represented  in  two  different  positions,  a lower- 
with  the  line  of  direction  L C,  and  a higher  with  the  line 
of  direction  U C.  Had  the  vehicle  not  been  high  laden, 
the  line  of  direction  would  have  remained  as  L C,  and  as 
it  falls  within  the  wheel  or  base,  the  vehicle  would  have 
maintained  its  balance,  but  being  now  laden  to  a consider- 
able height,  the  line  has  risen  to  about  the  place  where  it 
is  marked  descending  from  C to  U,  beyond  the  base;  con- 
sequently the  vehicle  must  overturn. 

188.  Children  who  have  not  gained 
experience  of  the  tendency  which  bodies 
have  to  be  overturned  when  their  centre 
of  gravity  is  wrong  placed,  frequently 
receive  falls  and  personal  injuries  by 
tumbling  from  pieces  of  furniture.  In 
the  annexed  cut,  figure  4,  a little  boy  is 
represented  standing  on  a chair,  and 
leaning  over  its  back.  So  long  as  the 
line  of  direction  from  A falls  within  the 
base  at  B.  he  is  safe;  but  if  he  lean 
much  farther  over,  and  cause  the  line  to 
fall  beyond  the  base,  to  C,  he  must 


Fig  4. 


174.  Explain  (he  drawing. 

175.  What  other  examples  are  cited  ? 


CENTRE  OF  GRAVITY. 


G5 


183.  Drunken  men,  who  reel  to  and  fro,  are  observed 
to  have  considerable  difficulty  in  preserving  their  erect 
position,  in  consequence  of  the  perpetual  disturbance  of 
their  centre  of  gravity.  Persons  who  feel  themselves  fall- 
ing, instinctively  throw  out  an  arm,  or  try  to  lean  in  an 
opposite  direction,  so  as  to  recover  their  balance.  For 
the  same  reason,  rope-dancers,  in  trying  to  balance  them- 
selves, use  a pole  loaded  at  each  end  with  a hall  of  lead  ; 
and  by  inclining  the  pole  in  the  direction  opposite  to  that 
to  which  they  feel  themselves  falling,  they  preserve  their 
equilibrium.  Some  dexterous  rope-dancers,  by  the  use 
of  their  arms  only,  are  able  to  maintain  their  balance. 

luO.  There  are  instances  in  which  bodies  will  not  be 
overturned,  although  the  line  of  direction  falls  consider- 
ably beyond  the  base.  These  exceptions  to  a common 
rule  are  observable  in  the  case  of  rapidly  and  smoothly 
moving  bodies,  in  which  centrifugal  force  acts  as  a counter- 
poise to  the  weight  of  the  body.  A fami  iar  example  of 
this  kind  occurs  in  the  case  of  skaters,  in  making  their 
circular  turns  on  the  ice,  in  which  they  bend  or  lean 
greatly  beyond  the  perpendicular  position  without  falling. 
A notice  of  this  peculiarity  in  moving  bodies  will  engage 
our  attention,  under  the  head  Centrifugal  Force. 

191.  The  tendency  which  leaning  bodies  have  to  fall, 
may  also  be  counteracted  in  some  measure  by  the  cohe- 
sion of  parts.  Thus,  there  are  many  instances  of  walls, 
steeples,  and  towers,  inclining  sensibly  from  the  vertical 
line,  and  yet,  by  the  strength  of  the  cement  which  binds 
them,  they  have  stood  for  ages. 

192.  Whatever  raises  the  centre  of  gravity,  or  narrows 
the  base,  allows  the  line  of  direction  to  pass  more  easily 
without  it,  and  diminishes  the  stability.  Hence  the  im- 
prudence of  rising  up  in  carriages  or  boats,  when  in 
danger  of  being  upset ; and  hence,  as  we  have  just 
mentioned,  the  danger  of  high-loading  of  vehicles.  Lately 
an  improvement  has  been  effected  in  stage-coach  build- 
ing, by  which  a chief  part  of  the  load  is  placed  as  low  as 


176.  What  exceptions  are  named? 

177.  What  useiul  hints  are  given  to  avoid  danger  ? 


66 


CENTRA  OF  GRAVITY. 


<he  axle  of  the  wheels ; and  by  this  means  the  danger  of 
overturning  is  almost  entirely  averted. 

193.  The  centre  of  gravity  of  a body  is  not  always  in 
the  substance  of  the  body.  Thus,  the  centre  of  gravity 
of  a circular  ring  is  in  the  centre  of  the  circle  ; of  an  ellip- 
tic or  oval  ring,  in 'the  centre  of  the  ellipse  ; and  of  a hol- 
low cylindric  tube,  it  is  in  the  imaginary  axis  of  the  tube. 
In  a drum,  for  instance,  the  centre  of  gravity  is  a point  in 
the  centre  of  the  drum,  where  there  is  nothing  but  air. 

194.  When  a circular  object  is  placed  on  level  ground, 
or  a horizontal  plane,  it  remains  at  rest  on  a point  of  its 
surface,  because  the  line  of  direction  from  its  centre,  which 
is  its  centre  of  gravity,  falls  perpendicularly  downwards 
to  the  point  on  which  it  is  in  contact  with  the  earth  and 
at  rest ; and  because  it  could  not  possibly  get  its  centre 
of  gravity  nearer  the  earth  by  changing  its  position. 

195.  When  a similar  circular  object  is  placed  on  an 
inclined  plane,  it  will  not  remain  at  rest,  but  roll  over, 
because  the  line  of  direction  from  its  centre  of  gravity  falls 
perpendicularly  downwards  in  front  of  the  point  on  its 
surface  which  touches  the  plane.  On  this  account  it  rolls 
over,  as  if  it  were  seeking  a spot  on  which  it  might  have 
the  line  of  direction  from  its  centre  of  gravity  passing 
through  its  point  of  contact  with  the  earth.  Hence  a 
circular  body  continues  rolling  down  an  inclined  plane  till 
it  find  a level  spot  on  which  the  line  of  direction  passes 
through  its  point  of  rest. 

190.  In  a bar  ol  iron,  six  feet  long,  and  of  equal  breadth 
and  thickness,  the  centre  of  gravity  is  just  three  feet  from 
each  end,  or  exactly  in  the  middle.  If  the  bar  be  sup- 
ported at  this  point,  it  will  balance  itself,  because  there 
are  equal  weights  on  both  ends.  This  point,  therefore,  is 
the  centre  of  gravity. 

197.  If  a bar  of  iron  be  loaded  at  one  end  with  a ball 
of  a certain  weight,  then  the  centre  of  gravity  will  not  be 
at  the  middle,  but  situated  near  the  heavy  end  of  the  bar. 
But  if  we  attach  a ball  of  the  same  weight  to  both  ends, 
the  centre  of  gravity  is  again  in  the  middle  of  the  bar. 


178.  VVh:.t  variations  in  the  centre  of  gravity  ? 

179.  Name  the  examples. 


CENTRE  OF  GRAVITY. 


67 


198.  A remarkable  illustration  of  the  principles  now  de- 
tailed, is  exhibited  in  the  case  of  the  earth  and  moon.  The 
earth  revolves  round  the  sun,  in  consequence  of  a cause 
already  explained,  namely,  the  sun’s  attraction;  but  in- 
stead of  the  centre  of  the  earth  describing  the  oval  or  el- 
liptic orbit  round  the  sun,  it  is  the  centre  of  gravity  of  the 
earth  and  moon  that  describes  it.  We  shall  briefly  ex- 
plain the  reason  for  this.  The  earth,  in  its  course,  is  en- 
cumbered with  the  moon,  a body  about  the  79th  of  its  mass  ; 
in  other  words,  the  moon  is  like  a small  ball  stuck  at  one 
end  of  a bar,  having  the  earth  or  a larger  ball  at  the  other 
end — the  bar  between  being  the  mutual  attraction  of  the 
earth  and  moon.  On  this  account,  the  centre  of  gravity 
of  the  earth  and  moon  is  at  a point  somewhere  between  the 
centres  of  the  earth  and  moon.  This  point  lies  not  far  be- 
low the  earth’s  surface.  Therefore,  if  the  earth  were  to 
fall  towards  the  sun,  it  would  be  this  point  which  would 
proceed  most  directly  towards  it. 

199.  In  suspending  an  irregularly  shaped  body  from 
different  points  successively,  we  may  learn  where  the 
centre  of  gravity  of  the  body  is  placed,  by  observing  that 

the  line  of  direction  in  each  case 
passes  through  the  same  point, 
which  point  is  the  centre  of  gra- 
vity. For  example,  let  a paint- 
er’s palette,  which  is  an  irregu- 
larly shaped  body,  be  suspended 
from  the  thumbhole,  as  in  the  an- 
nexed cut,  figure  5,  and  the  line 
of  direction  will  necessarily  be 
from  A to  B.  Next  suspend  it 
from  a point  at  D,  and  anew  line 
of  direction  will  be  obtained,  cross- 
ing the  line  A B.  The  place  where  the  two  lines  inter- 
sect, is  thus  the  centre  of  gravity.  The  point  of  suspension, 
on  being  removed  to  C,  will  give  the  same  place  of  inter- 
section in  the  original  line  of  direction  ; and  a similar  result 
will  follow  any  other  change  of  the  suspension  point. 


180  What  is  said  of  the  earth  and  moon  ? 
181.  Explain  the  drawing- 


68 


CENTRE  OF  GRAVITY . 


200.  In  the  various  natural  structures  displayed  in  the 
animal  and  vegetable  kingdoms,  the  centre  of  gravity  s 
always  so  situated  as  to  produce  a just  equilibrium  and  a 
harmony  of  parts.  Every  animal  is  properly  balanced  on 
its  limbs,  and  every  tree  has  a tendency  to  grow  in  a di- 
rection perpendicular  to  its  base,  whether  it  grow  from  a 
level  or  an  inclined  plane.  Some  animals  are  enabled  to 
move  in  opposition  to  the  law  of  gravity,  as,  for  instance, 
flies  creeping  on  the  ceiling  of  an  apartment ; but  in  such 
cases,  other  powers  in  nature  are  exerted  to  preserve  the 
secure  footing  of  the  animals. 

201.  Our  perceptions  and  appreciations  of  the  beautiful, 
both  in  nature  and  art,  appear  very  much  to  depend  on  the 
objects  we  contemplate  being  constructed  in  reference  to 
the  preservation  of  their  equilibrium  or  balance.  An  er  ct 
or  properly  balanced  man,  wall,  steeple,  and  pillar,  are 
more  grateful  to  the  sense  of  sight,  than  if  they  were  lean- 
ing to  a side.  We  feel  as  if  an  object  in  leaning  were 
doing  a violence  to  nature.  Thus,  the  sight  of  lines  and 
objects  swayed  from  the  perpendicular,  in  a ship  agi- 
tated by  the  waves,  disturbs  all  our  preconceptions  of 
what  is  consistent  with  nature,  and  powerfully  assists 
in  bewildering  our  senses,  and  rendering  us  sea-sick. 

202.  In  consequence  of  this  strong  perception  of  the 
beautiful  and  pleasing,  not  to  speak  of  the  absolute  utility, 
in  perpendicularly  erected  structures,  allartizans  employed 
in  building  are  anxious  to  preserve  the  true  line  of  per- 
pendicularity. For  this  purpose  they  have  continual  re- 
course to  what  they  call  a plumb-line  ; that  is,  a cord  with 
a small  ball  of  lead,  or  plummet,  at  its  lower  end,  hung  in 
a wooden  frame;  and  this  being  applied  to  the  edges  of 
the  structure  as  it  proceeds,  shows  whether  the  true  per- 
pendicular line  is  preserved.  Walls  leaning  from  the 
erect  position,  are,  from  this  useful  instrument,  said  to  be 
off  the  plumb-line. 


182.  What  is  said  of  animal  and  vegetable  structure  1 

183.  What  of  beauty  in  nature  and  art  ? 

184.  How  is  sea-sickness  accounted  for  in  part  ? 

185.  How  is  perpendicular  secured  by  builders  ? 


THE  PENDULUM. 


69 


THE  PENDULUM. 


203.  Gravity,  which  causes  bodies  to  fall,  also  causes 
them  to  swing  backwards  and  forwards,  when  suspended 
freely  by  a string  or  rod,  from  a point,  and  when  once 
moved  to  a side,  to  give  them  an  occasion  of  falling.  A 
body  suspended  in  this  manner  is  called  a Pendulum. 

204.  Pendulums  usually  consist  of  a rod  or  wire  of 
metal,  at  the  lower  end  of  which  a heavy  piece  or  ball  of 
brass  or  other  metal  is  attached.  When  a pendulum  swings, 
it  is  said  to  oscillate  or  vibrate  ; and  the  path  which  its  ball 
pursues  in  swinging,  from  its  resemblance  in  figure  to  an 
inverted  arch  or  how,  is  called  its  arc. 

205.  In  the  accompanying  cut,  figure  6,  a pendulum 

Fig.  g.  of  the  most  common  construction  is 


the  pendulum  is  at  rest,  it  hangs  perpendicularly,  as  here 
represented,  and  the  place  which  the  ball  is  seen  to  occupy 
is  called  the  point  of  rest. 

206.  The  pendulum  remains  at  rest  till  its  bail  is  drawn 
aside  to  allow  it  an  opportunity  of  swinging  on  its  axis. 
Being  raised  to  any  height  on  one  side,  and  set  at  liberty, 
the  ball,  by  the  force  of  gravity,  has  a tendency  to  fall  to 
the  ground,  but  being  confined  by  the  suspending  rod,  it 
is  compelled  to  make  a sweep  to  that  point  where  it  was 
formerly  hanging  at  rest,  immediately  beneath  the  point 
of  suspension.  But  it  does  not  stop  here  ; it  has  acquired 
a velocity  sufficient  to  carry  it  onward  in  an  ascending 
course  to  nearly  as  high  a point  on  the  opposite  side  as 
that  from  which  it  was  let  fall.  Of  its  own  accord,  it 


A 


represented.  A is  the  axis  or  point 
of  suspension.  B is  the  rod.  C is 
the  ball,  or  a round  flatfish  piece  of 
metal,  which  is  fastened  to  the  rod  by 
a screw  behind,  and  by  which  screw 


B 


Q 


✓ -it  can  be  raised  or  lowered  on  the  rod. 
D D is  the  path  or  arc  which  the 
ball  traverses  in  swinging.  When 


186.  Define  a pendulum,  and  expldn  the  drawing. 
181.  What  of  its  motion,  and  way  does  it  cease  ? 


70 


ISOCHRON’S}!  IN  PENDULUMS. 


again  falls  downwards  in  the  same  arc,  and  rises  ro  near 
the  point  where  it  set  off;  and  thus,  of  itself,  c niinu  s to 
swing  to  and  fro,  or  vibrate,  for  a certain  length  of  time, 
till  its  force  is  expended,  and  it  finally  comes  to  a state  of 
rest  in  its  original  dependent  situation  under  the  point  of 
suspension. 

217.  At  every  sweep  of  the  pendulum  (when  not  med- 
dled with,  or  assisted  by  any  external  force),  the  length 
of  the  path  or  arc  traversed  by  the  ball  is  in  a small  degree 
diminished.  This  arises  from  two  causes — the  obstruction 
offered  by  the  atmosphere,  and  the  friction  on  its  axis  or 
point  of  suspension.  These  causes,  therefore,  sooner  or 
later,  bring  the  pendulum  to  a state  of  rest,  unless  external 
force  of  some  kind  continues  to  be  applied  to  urge  it  to  sus- 
tain its  action. 

208.  The  ball  of  a pendulum  in  swinging,  as  has  been 
mentioned,  describes  the  figure  of  an  arc.  This  arc  is  a 
certain  porth  n of  a circle.  The  extent  of  this  portion  de- 
pends on  the  force  exerted  in  setting  the  pendulum  in  mo- 
tion, or  in  drawing  it  aside  to  let  it  fall.  A circle  being 
divided  by  mathematicians  into  3 0 degrees  or  parts,  the 
ball  may  be  made  to  swing  over  five,  ten,  twenty,  or  any 
other  number  of  degrees  under  ISO,  which  is  half  a circle. 
The  extent  of  the  arc  traversed  under  ordinary  circum- 
stances, is  from  ten  to  twenty  degrees. 

209.  When  the  ball  of  a pendulum  traverses  an  arc  not 
exceeding  four  or  five  degrees,  it  is  observed  to  possess 
what  is  called  the  property  of  isochrortism — that  is,  it 
passes  over  its  point  of  rest  always  at  the  same  interval  of 
time  (or  very  nearly  the  same  interval),  whether  it  traverse 
one,  two,  three,  four,  or  five  degrees  ; thus  always  accom- 
plishing its  excursion  in  precisely  the  same  space  of  time. 
At  first  sight  this  seems  doubtful ; but  a consideration  of 
circumstances  shows  that  it  is  perfectly  correct.  The 
cause  of  the  phenomenon  is,  that  the  pendulum  which 
goes  over  a greater  exent  of  arc,  has  a greater  speed  than 
that  which  goes  over  a smaller  extent.  It  should,  how- 
ever, be  clearly  understood,  that  the  comparison  as  to 


188.  What  of  isorhronisns  T 


rt.O'M  PENDUl.TTMS. 


71 


lengths  of  time  occupied  in  vibration,  alluded  to  here,  ap- 
plies only  to  any  given  length  of  rod — that  is  to  say,  we 
must  not  compare  the  time  occupied  by  a long  rod  with 
the  time  occupied  by  a.  short  rod  ; but,  in  every  case,  hold 
to  only  one  rod,  whatever  be  its  length. 

210.  A pendulum  with  a long  rod  vibrates  slower  than 
one  with  a short  rod.  The  time  does  not  become  longer, 
however,  in  exact  proportion,  as  we  extend  the  rod.  The 
vibration  it  must  always  be  recollected,  is  analogous  to  the 
falling  bodies.  The  spaces  fallen  through  by  a body  in 
1,  2,  3,  or  4 seconds,  are  not  in  proportion  to  1,  2,  3,  4, 
and  so  on,  but  in  the  proportion  of  1,  4,  9,  16,  25,  and 
so  on,  or  the  squares  of  the  time  occupied  in  falling. 
In  the  case  of  pendulums,  it  is  found  that  their  lengths 
are  as  the  squares  of  the  times  of  vibration.  Thus,  if  the 
times  occupied  by  one  vibration  of  two  pendulums  be  1 and 
2 seconds  respectively,  the  lengths  of  the  pendulums  will 
be  as  1 and  4 ; so  if  the  time  of  one  vibration  of  several  pen- 
dulums be  as  1,  2,  3,  4,  their  lengths  are  as  1,  4,  9,  and  16. 

211.  The  vibrations  of  the  pendulum  being  produced  by 
terrestrial  gravitation,  it  follows,  as  a natural  result,  that  if 
the  force  of  gravitation  be  weakened,  so  will  the  tendency 
of  the  ball  of  the  pendulum  to  fall  or  swing  be  weakened. 
This  result  is  distinctly  observable  in  different  parts  of  the 
earth.  At  the  equator,  the  earth,  as  already  mentioned, 

, bulges  out  to  a thickness  of  26  miles  on  the  diameter,  or 
13  miles  from  the  surface  to  the  centre  ; and  as  the  attrac- 
tion of  gravitation  proceeds  from  the  centre,  the  force  of 
this  attraction  is  consequently  weaker  at  the  surface  at  the 
equator  than  it  is  at  the  surface  at  the  poles.  At  every 
part  of  the  surface  between  the  equator  and  poles,  there  is 
a proportionate  increase  of  gravity.  Besides  the  effect 
produced  by  the  greater  distance  of  the  surface  from  the 
centre  at  the  equator,  centrifugal  force,  which  is  strongest 
at  the  equator,  assists  in  weakening  the  attractive  force  at 
that  place. 

212.  In  consequence  of  these  combined  causes,  a pen- 

189.  How  does  the  length  of  rod  affect  time  ? 

190.  What  difference  occurs  over  the  equator  and  whv  ? 

191.  By  what  rule  is  the  length  of  the  pendulum  varied? 


72 


CENTRE  OF  OSCILLATION'. 


dulum  of  a given  length  vibrates  more  slowly  at  the  equa- 
tor than  at  the  poles.  In  proportion  as  we  advance  on  the 
surface  of  the  earth  from  the  equator  towards  the  poles,  so 
does  the  pendulum  swing  or  vibrate  more  quickly.  In 
order,  therefore,  to  preserve  uniformity  of  speed  in  pendu- 
lums at  different  parts  of  the  globe — that  is,  in  order  that 
they  may  all  vibrate  in  one  second,  their  length  must  be 
regulated  according  to  the  distance  of  the  places  from  the 
equator.  Thus,  each  degree  of  latitude  has  its  own  length 
of  pendulum. 

213.  The  uniform  vibration  of  the  pendulum  has  ren- 
dered it  useful  in  regulating  the  motion  of  clocks  for  mea- 
suring time.  In  the  common  clock,  a pendulum,  con- 
nected with  the  wheel-work,  and  impelled  by  weights,  oi 
a spring,  regulates  the  motions  of  the  minute  and  hour 
hands  on  the  dial-plate,  by  which  the  time  of  day  is  pointed 
out.  If  no  pendulum  were  employed,  the  wheels  would  go 
very  irregularly.  The  pendulum  is  regulated  in  length, 
so  as  to  vibrate  sixty  times,  each  time  being  a second,  in 
the  space  of  a minute.  At  each  vibration,  it  acts  upon 
the  tooth  of  awheel,  which  turns  the  rest  of  the  machinery. 
In  order  that  the  pendulum  may  vibrate  neither  quicker 
nor  slower  than  sixty  times  a minute,  in  the  latitude  of 
London  it  must  measure  39  inches  and  about  the  7th  of 
an  inch  from  the  point  of  suspension  to  the  centre  of  os- 
cillation. A pendulum  at  Edinburgh  would  require  to  be 

a small  degree  longer.  The  greatest  possible  nicety  is  ’ 
required  in  the  adjustment  of  the  length  ; for  a difference 
in  extent  amounting  to  the  1000th  part  of  an  inch,  would 
cause  an  error  of  about  one  second  in  a day.  Therefore, 
to  make  a pendulum  go  slower  by  one  second  a day,  it 
must  be  lengthened  by  the  1000th  part  of  an  inch ; and  to 
make  it  go  quicker,  it  must  be  shortened  in  the  same  pro- 
portion. 

214.  It  is  possible  to  cause  short  pendulums  to  regu- 
late the  movement  of  clocks  the  same  as  long  pendulums  : 
and  this  is  done  in  -cases  where  long  pendulums  would  be 
inconvenient,  or  inelegant  in  appearance.  This  is  accom- 


192.  Des  ribe  he  use  of  pendulums  in  clock-  and  iheir  varie  y. 


CENTRE  OF  OSCILLATION. 


73 


plished  by  shortening  the  pendulum  to  a fourth  of  its  or- 
dinary length,  by  which  it  beats  or  vibrates  twice  instead 
of  once  in  a second.  The  wheel-work  is  constructed  to 
suit  this  arrangement. 

215.  The  pendulums  of  clocks  being  made  of  a rod  of 
metal,  they  are  liable  to  be  extended  by  the  heat  of  sum- 
mer and  shortened  by  the  cold  of  winter ; and  by  this 
means  the  uniformity  of  their  motion  is  destroyed.  Vari- 
ous contrivances  have  been  adopted  in  order  to  compen- 
sate this  effect  on  the  motion  of  the  clock,  and  pendulums 
constructed  for  this  purpose  are  called  compensation  pen- 
dulums. The  parts  of  the  rods  of  these  pendulums  are 
so  constructed  and  arranged  that  when  one  of  them  ex- 
pands downwards,  another  at  the  same  time  expands  up- 
wards, by  which  any  variation  from  temperature  is  greatly 
diminished. 

216.  In  the  moving  mass  of  every  pendulum,  there  is 
a point  which  is  called  the  centre  of  oscillation.  The 
centre  of  oscillation  may  be  in  the  rod  or  in  the  ball,  or 
even  below  the  pendulum,  according  to  circumstances. 
To-  understand  this,  it  will  be  necessary  to  remember,  that, 
if  each  particle  of  matter  in  the  swinging  body  were  at 
liberty  to  swing  separately,  those  particles  which  are  near 
the  axis  would  swing  more  rapidly  than  those  which  are 
farther  rem  -ved  from  it.  Although  the  various  compo- 
nent particles,  from  their  intimate  connection  with  each 
other,  are  not  at  liberty  to  obey  this  tendency,  still  the 
tendency  exists.  The  nearer  particles  are  retarded  by 
those  more  distant,  and  those  which  are  distant  are  accele- 
rated by  those  which  are  nearer.  There  is  thus  a mutual 
exchange  of  influences  among  the  particles  of  the  swing- 
ing body.  But  there  is  a point  or  spot  somewhere  in  the 
mass,  where  the  mutual  exchange  is  so  completely  equal- 
ized, that  the  influences  or  momenta  neutralize  each  other, 
and  the  particle  of  matter  situated  at  this  point  con- 
sequently swings  as  if  unconnected  with  any  other  par- 
ticle in  the  body.  This  point  is  the  centre  of  oscillation. 


193.  Whence  the  necessity  of  compensation  pendulums  ? 

194.  Whai  of  the  centre  of  oscillation  ? 


74 


CENTRE  OF  OSCILLATION. 


217.  The  centre  of  oscillation  in  a pendulum  is  disco- 
verable in  the  following  manner.  Take  a common  p n- 
dulum  and  set  it  a-swinging.  Next,  take  a small  ball  of 
lead  and  suspend  it  by  a fine  thread  from  the  same  axis 
as  that  of  the  pendulum.  This  ball  and  thread  form  what 
is  called  a simple  pendulum.  It  is  simple,  because  the 
weight  of  the  thread  may  be  reckoned  as  nothing,  and 
the  ball  vibrates  with  the  smallest  possible  resistance  or 
impediment;  by  which  means  it  is  well  lilted  for  experi- 
ments. This  simple  pendulum  is  set  a-swinging  in  front 
of  the  common  pendulum,  and  its  thread  must  be  length- 
ened or  shortened,  as  may  be  necessary,  to  cause  the 
leaden  ball  to  move  at  precisely  the  same  pace  or  velocity 
as  that  of  the  common  pendulum.  Having  rendered  the 
two  velocities  exactly  uniform,  then  stop  both  the  pendu- 
lums, and  the  centre  of  the  spot  on  the  common  pendu- 
lum, which  the  ball  covers  (supposing  the  ball  to  he  per- 
fectly circular),  is  the  centre  of  oscillation. 

218.  It  is  to  be  noted,  that  the  discovery  of  the  centre 
of  oscillation  is  not  a matter  of  practical  utility,  as  far  as 
regards  common  or  clock  pendulums,  but  is  interesting  in 
a philosophical  point  of  view,  from  the  mechanical  truths 
connected  with  it.  For  example,  if  we  take  a straight 
and  uniformly  thick  bar  of  wood  or  metal,  and  suspend  it 
in  the  character  of  a pendulum,  we  shall,  by  the  means 
just  pointed  out,  ascertain  that  its  centre  of  oscillation  is 
at  a certain  spot.  If  we  then  take  the  pendulum  from  its 
axis,  reverse  it,  and  suspend  it  from  the  spot  indicated, 
we  shall  perceive,  that,  on  being  set  in  motion,  it  will 
again  swing  in  agreement  with  the  leaden  ball  and  thread. 
The  centre  of  oscillation  and  the  point  of  suspension  are 
thus  said  to  be  controvertible,  without  producing  any 
change  in  the  rate  of  vibration.  How  this  result  should 
follow,  appears  at  first  rather  strange,  but  on  consideration 
it  will  be  found,  that,  by  reversing  the  pendulum,  there  is 
a portion  necessarily  placed  above  the  axis;  wherefore, 
the  speed  which  would  ensue  from  the  shortening  of  the 


195.  How  is  this  centre  ascertained  ? 

196.  Of  what  importance  is  this  experiment  ? 


LAWS  OF  MOTION. 


75 


pendulum  is  counterbalanced  by  the  retarding  influence 
of  the  portion  placed  above  the  axis. 

THE  LAWS  OF  MOTION. 

219.  Motion,  as  already  mentioned,  is  the  changing  of 
place  or  the  opposite  of  rest.* 

220.  According  to  the  general  explanations  which  have 
been  given,  it  appears  that  motion  in  bodies  is  as  natural 
as  rest,  and  that  matter  passively  submits  to  remain  in 
either  of  these  states  in  which  it  may  be  placed,  provided 
no  external  force  or  obstacle  interfere  to  cause  an  alteration 
of  condition. 

221.  These  and  other  fundamental  laws  of  nature,  in 
relation  to  rest  and  motion  of  matter,  are  laid  down  by 
Sir  Isaac  Newton  in  the  following  three  propositions  : — 

1st,  Every  body  must  persevere  in  its  state  of  rest,  or  of 
uniform  motion  in  a straight  line,  unless  it  be  compelled 
to  change  that  state  by  forces  impressed  upon  it. 

2d,  Every  change  of  motion  must  be  proportional  to  the 
impressed  force,  and  must  be  in  the  direction  of  that 
straight  line  in  which  the  force  is  impressed. 

3d,  Action  must  always  be  equal  and  contrary  to  reac- 
tion : or  the  actions  of  two  bodies  upon  each  other  must 
be  equal,  and  their  directions  must  be  opposite. 

222.  These  propositions  we  shall  treat  separately.  In 
the  first  of  the  series  there  are  three  points  requiring  con- 
sideration, namely,  the  permanency,  the  uniformity,  and 
the  straight  line  of  direction,  of  motion  in  bodies. 

UNIFORM  MOTION  IN  A STRAIGHT  LINE. 

223.  As  was  formerly  observed,  it  is  impossible  to 
show  either  permanency  or  uniformity  of  motion  in  bodies 

* In  scientific  language,  the  nature  and  laws  of  motion  form  a branch 
of  knowledge  called  Dynamics  (a  word  signifying  power  or  force) ; 
while  the  principles  of  forces  in  equilibrium  are  classed  under  the  term 
Statics  (a  word  signifying  to  stand  or  be  at  rest). 


197.  Name  Newton’s  three  propositions. 

198.  What  considerations  are  important  in  the  first  ? 

199.  Where  are  the  laws  of  motion  most  clearly  illustrated  ? 

200.  Define  Dynamics  and  Statics. 


70  UNIFORM  MOTION  IN  A STRAIGHT  LINE. 

upon  or  near  the  earth  ; for  all  moving-  bodies  are  sooner 
or  later  brought  to  a state  of  rest  by  the  force  of  attrac- 
tion, friction,  and  the  opposition  of  the  atmosphere.  It  is 
only,  therefore,  in  the  case  of  the  great  works  of  nature 
or  planetary  bodies,  that  the  laws  of  motion  are  most 
clearly  and  fully  illustrated.  In  them,  motion  is  uniform 
and  permanent.  The  earth,  for  example,  moves  at  the 
present  moment  with  the  same  regularity,  the  same  pla- 
cid steadiness,  that  it  did  thousands  of  years  ago.  On 
account  of  this  regularity  and  permanency  of  motion,  as- 
tronomers are  able  to  calculate  eclipses  of  the  sun,  moon, 
or  other  heavenly  bodies,  at  any  distance  of  time.  They 
can  foretell,  to  an  instant  of  time,  at  what  part  of  their  orbits 
the  earth  or  moon  will  be  a thousand  years  hence.  The 
motions  of  the  planetary  bodies  also  afford  a standard 
wherewith  to  reckon  the  course  of  time.*  We  call  the 
space  of  time  occupied  by  a revolution  of  the  earth  in  its 
orbit  round  the  sun,  a year — that  of  a revolution  of  the 
earth  on  its  axis,  a day — that  of  a revolution  of  the  moon 
round  the  earth,  a month  ; and  these  periods  we  divide 
into  weeks,  hours,  minutes,  and  seconds.  Thus,  time  is 
sectioned  and  computed  with  unerring  accuracy.  The 
inhabitants  of  the  different  planets,  in  all  likelihood,  take 
advantage  of  the  same  means  of  reckoning  their  time,  each 
planet,  however,  having  its  own  peculiar  length  of  year  and 
day,  according  to  the  period  occupied  in  its  revolution 
round  the  sun  or  on  its  axis.  In  Jupiter,  the  year  is 
nearly  12  of  our  years,  and  the  length  of  the  day  nearly 
10  hours.  In  Mars,  the  year  is  1 of  our  years  and  321 
days,  and  the  day  24  hours  and  39  minutes.  In  Venus, 

* The  motions  of  the  planetary  bodies  are  here  spoken  of  as  being 
uniform  or  regular;  this  is  not  strictly  correct.  When  we  come  to 
treat  of  Astronomy,  it  will  be  shown  that  there  are  certain  irregulari- 
ties in  the  motions  of  the  planets,  caused  by  their  action  on  each  other ; 
but  as  these  irregularities  are  the  subject  of  calculation,  and  do  not 
disturb  the  harmonious  permanency  of  motion  in  the  system  of  the 
universe,  it  has  been  thought  unnecessary  to  advert  to  them  in  the  above 
popular  definition. 


201 . How  is  time  reckoned  by  the  motions  of  the  planets! 

202.  What  of  motion  in  a straight  line  ? 


CENTRIFUGAL  FORCE  AND  CIRCULAR  MOTION.  77 

the  year  is  only  224  of  our  days,  and  the  day  23  hours  and 
21  minutes. 

224.  The  tendency  of  a body  to  move  in  a straightdine 
from  the  point  whence  it  set  out,  is  as  much  a property  of 
matter  as  the  uniformity  of  motion.  If  we  conceive  the 
idea  of  a body  impelled  into  a state  of  motion  by  any  given 
force,  and  at  the  same  time  conceive  the  idea  that  there  is 
no  obstacle  to  interrupt  it,  no  attractive  force  to  bend  it 
aside,  we  shall  then  fully  understand  that  a moving  body 
must,  as  a matter  of  necessity,  from  its  property  of  inertia, 
proceed  in  a straight  line  of  direction — it  must  go  on  an 
even  path  for  ever. 

CENTRIFUGAL  FORCE  AND  CIRCULAR  MOTION. 

225.  Bodies  in  flying  round  a centre  have  a tendency 
to  proceed  in  a straight  line,  and  this  principle  of  motion, 
as  already  mentioned,  is  termed  centrifugal  force.  Ex- 
amples of  this  tendency  are  very  familiar  to  our  observa- 
tion. When  we  whirl  rapidly  a sling  with  a stone  in  it, 
and  suddenly  allow  the  stone  to  fly  off,  it  proceeds  at  first 
in  a straight  line,  but  is  gradually  pulled  to  the  earth  by 
attraction.  In  turning  a circular  grinding-stone  rapidly 
with  water  in  contact  with  it,  we  perceive  a rim  of  water 
first  rising  on  the  stone  and  next  flying  off ; and  the  more 
rapidly  we  turn  the  stone,  so  does  the  water  fly  off  with 
the  greater  force.  I'n  grinding  corn  by  two  rapidly  turn- 
ing stones  playing  on  each  other,  the  grain  poured  in  at 
an  opening  at  the  centre  is  quickly  shuffled  towards  the 
edges  of  the  stones  and  expelled  in  the  condition  of  meal 
or  flour.  If  we  put  some  water  in  a vessel,  and  rapidly 
turn  it  in  one  direction,  we  shall  find  that  the  water  en- 
deavours to  escape,  and  rises  up  to  the  edges  of  the  vessel, 
leaving  a deep  hollow  in  the  middle.  The  tendency  to  fly 
off  from  a centre  is  made  use  of  in  the  manufacture  of  pot- 
tery : Soft  clay  being  placed  on  a revolving  wheel,  it  quick- 
ly spreads  towards  the  circumference  of  the  machine,  and 
is  guided  or  moulded  by  the  hand  of  the  potter  into  the 


203.  What  of  centrifugal  force  ? examples. 

204.  What  manufactures  are  on  this  principle  ? 


78  CENTRIFUGAL  FORCE  AND  CIRCULAR  MOTION. 

required  form.  In  forming  common  crown  or  window 
glass,  advantage  is  also  taken  of  the  principle  of  centrifugal 
force.  A thick  round  mass  of  glass,  softened  by  heat  and 
fixed  at  the  middle  on  an  iron  rod,  being  made  to  turn  ra- 
pidly round  first  in  one  direction,  and  then  in  the  opposite, 
and  continuing  this  alternating  rotary  motion  till  the  glass 
becomes  cool,  is  found  to  spread  out  into  a large,  thin,  cir- 
cular plaie.  From  this  plate,  square  panes  of  glass  are 
afterwards  cut. 

226.  Equestrians,  in  performing  their  feats  of  horseman- 
ship, always  incline  their  bodies  inwards  when  standing 
on  a horse  which  is  running  round  a circle.  Centrifugal 
force  having  a tendency  to  impel  them  outwards,  is  thus 
counteracted  by  the  inward  leaning,  and  forms  a species 
of  support  to  their  overhanging  bodies.  A horse  running 
in  a circle,  or  quickly  turning  a corner,  naturally  adopts 
the  same  count.,  racting  posture,  and  leans  inwards.  A 
skater,  in  moving  in  a circular  or  curvilin  ar  path  on 
smooth  ice,  also  leans  inwards,  so  much  so,  that  if  he 
were  to  stand  still  in  this  posture,  he  would  inevitably  fall 
on  his  side  ; but  centrifugal  force,  which  has  a tendency 
to  impel  his  body  outwards  from  the  curve,  or  in  a straight 
line  of  motion,  sustains  him,  as  it  does  the  equestrian,  and 
he  therefore  moves  gracefully  and  safely  in  the  circular 
path  which  his  fancy  directs.  In  this  and  other  instances, 
we  find  the  force  of  gravity  overcome  by  centrifugal  force. 
It  is  in  obedience  to  this  principle,  that  the  earth  bulges 
out  to  the  thickness  of  2(5  miles  upon  the  circumference 
at  the  equator,  where  the  whirling  motion  is  most  rapid. 

227.  Thus  centrifugal  force  is  the  tendency  to  fly  ofF 
in  a straight  line,  or  at  a tangent,  from  motion  round  a 
centre;  and  the  power  which  prevents  bodies  from  flying 
off,  and  draws  them  towards  a centre,  is,  as  already  men- 
tioned, called  centripetal,  or  centre- seeking  force.  All 
bodies  moving  in  circles  are  constantly  acted  upon  by  these 
opposite  forces,  as  may  be  exemplified  by  the  annexed  cut, 
fig.  7.  A is  a point  to  which  a string  with  a ball  at  the  end 


205.  Name  the  o:her  illustrations  here  cited. 
20;  >.  What  of  centripetal  force  ? 


REVOLVING  BODIES.  71) 

of  it,  B,  is  attached.  On  forcing 
the  ball  B into  motion,  it  will  de- 
scribe a circle  round  the  point  A, 
in  which,  case  the  string  is  the 
centripetal  force.  The  ball  in 
whirling,  however,  having  a con- 
tinual tendency  to  fly  off,  if  it  be 
disengaged  from  the  string  at  C, 
will  go  in  a straight  line  C D ; if 
at  E,  it  will  go  in  the  line  E F ; if 
at  G,  in  the  line  G H ; and  soon, 
at  every  point  in  the  circle. 

228.  The  mutual  action  of  centrifugal  and  centripetal 
forces,  in  the  case  of  circular  motion,  proceeds  according 
to  a certain  ratio.  If  the  mass  of  the  revolving  body  be 
increased,  its  distance  from  the  centre  and  velocity  remain- 
ing the  same,  its  centrifugal  force  will  be  increased  in  the 
same  proportion.  If  the  distance  from  the  centre  be  in- 
creased, while  the  mass  and  the  time  of  revolution  remain 
the  same,  the  centrifugal  force  will  also  be  increased  in 
the  same  proportion.  If  the  number  of  revolutions  per- 
formed in  a given  time  be  twice  as  many,  the  distance  and 
mass  being  unchanged,  the  centrifugal  force  will  be  four 
times  as  great ; if  three  times  as  many,  the  force  will  be 
nine  times  as  great ; if  four  times  as  many,  it  will  be  six- 
teen times  as  great ; and  so  on  in  the  same  proportion. 
The  masses  of  the  planets,  and  their  distances  from  the 
sun,  being  various,  the  forces  which  affect  them  are  also 
similarly  varied. 

229.  The  line  round  which  a body  performs  a motion 
of  rotation,  is  called  an  axis.  This  axis  may  be  only  ima- 
ginary, like  that  of  the  earth ; or  real,  as  the  axle  of  a 
wheel.  The  body  may  revolve  about  two  projecting  pins 
or  pivots  resting  in  sockets,  in  which  case  its  axis  is  a 
straight  line  joining  the  pivots  ; or  it  may  turn  on  a cylin- 
drical rod  of  small  diameter,  passing  through  the  body,  like 
a wheel  on  its  axle.  It  is  evident  that  every  point  of  the  body, 


Fig.  7. 


207.  Explain  the  diagram. 

203.  What  of  the  mutual  action  of  these  two  forces  ? 
209.  What  ot  the  axis  ? 


80 


REVOLVING  BODIES. 


during  its  revolution,  will  describe  a circle,  the  centre  of 
which  is  a point  in  the  axis  of  the  body. 

230.  In  the  turning  of  a wheel 
on  its  axis,  that  part  which  is  at  the 
greatest  distance  from  the  centre 
has  the  greatest  velocity  ; and  at 
this  extremity  of  the  circumference, 
the  centrifugal  force  is  greatest.  For 
example,  in  the  representation  of  a 
wheel  with  arms  radiating  from  a 
centre,  (figure  8,)  the  velocity  is 
greater  at  the  extremity  of  the  arm 
at  A,  than  it  is  at  B,  half  tin-  distance  from  the  centre.  But 
the  point  B goes  round  as  often  as  the  point  A.  having  a 
smaller  circle  to  traverse. 

231.  In  this  manner,  the  velocity  of  revolving  bodies 
must  always,  as  a matter  of  necessity,  increase  in  propor- 
tion to  the  distance  from  the  centre  of  motion.  Hence  a 
comparatively  small  centrifugal  force  near  the  centre,  is 
prodigiously  increased  towards  the  circumference.  By  in- 
creasing the  force,  and  adding  to  the  velocity  of  a revolv- 
ing body,  the  centrifugal  force  becomes  so  great  that  it 
will  in  some  cases  overcome  the  cohesiveness  in  the  ma- 
terial of  the  body,  and  cause  it  to  break  and  fly  off  in 
pieces.  When  grinding-stones  are  thus  whirled  with  great 
rapidity,  they  are  apt  to  be  destroyed,  flying  in  pieces  to  the 
extreme  danger  of  those  who  are  using  them. 

232.  The  power  of  centrifugal  force  in  rapidly  whirl- 
ing bodies,  may  be  rendered  so  great  as  to  overcome  the 
force  of  gravity.  In  whirling  a sling  with  a stone  in  it, 
the  stone  does  not  fall  out  of  its  place  in  the  sling.  The 
following  is  a more  striking  example  : — Place  a jug  of 
water  on  the  inside  of  the  rim  of  a wheel  a few  feet  in 
diameter;  then,  beginning  gradually,  set  the  wheel  in 
rapid  motion,  and  it  will  be  observed  that  the  jug  retains 
its  place,  whirling  round  in  a perfectly  stable  manner,  and 
that  even  the  water  in  it  is  not  spilled.  Thus,  gravity,  or 
the  tendency  to  fall  downwards,  is  overcome  by  centrifugal 

210.  Explain  the  diagram. 

211.  What  of  increased  velocity  ? 


Fift  8. 


REVOLVING  BODIES. 


81 


force.  If  the  jug  were  placed  in  a situation  in  the  wheel, 
near  the  centre  of  motion,  where  the  centrifugal  force  is 
weak,  it  would  at  once  fall  to  the  ground. 

233.  When  the  axis  of  a revolving  body  is  imaginary, 
it  is  sometimes  in  motion  itself,  like  the  axis  of  the  earth. 
In  most  cases  of  rotary  motion,  the  axis  is  immovable, 
and  the  motion  always  in  one  direction,  as  the  wheels  of 
watches,  clocks,  and  machinery ; and  in  some  cases  the 
motion  is  alternating  or  reciprocating,  as  the  vibrations  of 
a pendulum,  the  oscillations  of  the  balance-wheel  of  a 
watch  or  chronometer,  or  the  working-beams  of  steam- 
engines  ; in  which  cases  the  motion  continues  in  one  direc- 
tion only  for  a short  period,  and  is  then  reversed.  This 
alternating  motion  is  called  oscillation  or  vibration. 

234.  When  a body,  which  is  quiescent  and  free,  as  a 
ball  lying  on  a perfectly  smooth  plane,  is  acted  on  by  an 
instantaneous  force,  and  in  the  direction  of  its  centre  of 
gravity,  the  body  will  be  impelled  with  a uniform  motion 
in  the  direction  of  the  stroke,  having  only  this  motion  of 
translation,  as  it  is  called,  without  any  motion  of  rotation. 
If  the  impulse  given  to  the  body  be  not  in  the  direction  of 
its  centre  of  gravity,  it  will  still  receive  the  same  motion 
of  translation,  but  it  will  also  have  communicated  to  it  a 
motion  of  rotation  about  its  centre  of  gravity.  In  this  case, 
each  of  the  two  motions  will  be  exactly  the  same  as  if  the 
other  did  not  exist.;  that  is,  the  progressive  motion  is  the 
same  as  if  the  direction  of  the  impulse  passed  through  the 
centre  of  gravity,  and  the  motion  of  rotation  is  just  what 
would  be  produced  by  the  same  impulse,  if  the  body  had 
a fixed  axis  through  its  centre  of  gravity,  and  about  which 
it  whirled. 

235.  There  is  a point  at  a certain  distance  from  the 
axis  of  a revolving  body,  at  which,  if  all  its  matter  were 
concentrated,  it  would  give  exactly  the  same  resistance 
to  the  communication  of  rotary  motion,  as  the  whole  body 
itself  does,  supposing  that  in  both  cases  the  same  impulse 
is  given,  and  at  the  same  distance  from  the  axis.  This 


212.  Will  this  force  overcome  gravity  ? 

213.  Describe  oscillation  and  other  forms  of  rotary  motion. 

214.  What  is  a motion  of  translation,  and  how  complicated  ? 


LAWS  OF  PROJECTILES. 


b2 

point  is  called  the  centre  of  gyration,  and  its  distance 
from  the  axis  is  called  the  radius  of  gyration.  This  centre 
of  gyration  is  analagous  to  the  centre  of  oscillation  in  vibrat- 
ing bodies.  The  product  of  the  number  representing  the 
mass  or  weight  of  a body  into  th#t  denoting  the  square  of 
the  length  of  this  radius,  is  called  the  moment  of  inertia. 
For  example,  let  a wheel  be  10  pounds  in  weight,  and  its 
radius  of  gyration  2 feet,  the  square  of  which  2 is  4 ; then 
multiply  10  by  4,  and  40  is  given  as  the  moment  of  inertia. 
The  word  moment,  used  in  this  sense,  is  a contraction  of 
momentum,  a term  which  in  this  respect  is  now  disused, 
in  order  to  prevent  its  being  confounded  with  momentum 
in  ordinary  moving  bodies. 

236.  If  the  parts  of  a body  be  symmetrically  distributed 
around  an  axis  of  rotation,  that  is,  if  equal  portions  of  the 
body  be  placed  at  equal  distances  from  it,  and  in  directly 
opposite  directions,  the  opposing  centrifugal  forces  will 
balance  each  other,  and  there  will  be  no  pressure  on  the 
axis,  and  the  body  would  revolve  permanently  about  it. 
Thus,  a sphere  of  uniform  density  would  revolve  perma- 
nently about  any  of  its  diameters.  A cylinder  of  uniform 
density  would  also  revolve  permanently  about  its  axis.  If 
the  revolving  body  be  not  uniform,  or  fairly  balanced  on  its 
imaginary  axis,  it  will  possess  an  irregular  or  hobbling 
motion,  and  come  sooner  to  a state  of  rest  by  friction 
than  would  be  the  case  if  it  were  of  regular  density, 
or  properly  balanced.  Examples  of  this  are  very  fami- 
liar. 


LAWS  OF  PROJECTILES. 

237.  Bodies,  on  being  projected  by  any  impulsive 
forces,  are  called  projectiles,  and  are  observed  to  pursue  a 
curvilinear  or  bent  line  of  direction  in  their  motion.  The 
bending  from  the  straight  line  is  produced  by  the  force  of 
gravity,  and  “the  change  is  proportional  to  the  impressed 
force.” 


215.  Explain  the  centre  and  radius  of  gyration. 

216.  What  of  the  moment  of  inertia? 

217.  What  of  the  uniformity  of  a revolving  body  ? 

218.  What  of  projectiles  ? 


LAWS  OF  PROJECTILES. 


83 


238.  A ball  projected  from  a cannon,  a stone  thrown  by 
the  hand,  and  water  spouted  from  a confined  vessel,  furnish 
familiar  examples  of  curvilinear  motion. 

239.  It  is  a remarkable  law  of  motion,  that,  whether 
the  force  which  projects  a body  be  great  or  small,  the  body, 
if  thrown  horizontally,  will  reach  the  surface  of  the  earth 
from  the  same  height,  in  the  same  space  of  time,  not  cal- 
culating resistance  of  the  air.  For  example,  if  two  guns 
are  fired  from  the  same  spot  at  the  same  instant,  and. in  a 
horizontal  direction,  one  of  the  balls  falling  half  a mile, 
and  the  other  a mile  distant,  it  will  be  found  that  the  ball 
which  proceeds  the  greatest  distance  takes  precisely  the 
same  time  to  reach  the  ground  which  the  other  does. 

240.  The  time  of  flight,  as  it  is  called,  of  two  balls, 
will  be  the  same  in  whatever  directions  and  with  whatever 
velocities  they  are  fired,  provided  they  reach  the  same 
height. 

241.  The  reason  for  the  same  length  of  time  being  oc- 
cupied  in  falling  by  both  balls,  is,  that  they  are  both  car- 
ried downward  at  the  same  rate  by  gravity.  Hence,  a 
ball  dropped  perpendicularly  from  the  top  of  a high  tower, 
does  not  reach  the  ground  sooner  than  a ball  shot  from  the 
same  height  to  the  distance  of  one  or  more  miles  in  a hori- 
zontal direction. 

242.  In  projecting  bodies  through  the  atmosphere,  great 
advantage,  in  point  of  distance,  is  gained  by  impelling 
them  from  heights,  because  a ball  thrown  from  a high 
situation  to  a lower,  reckoning  its  whole  course,  is  more 
aided  than  retarded  by  gravity.  When  the  ball  is  pro- 
jected from  a lower  situation  to  a higher,  it  is  in  the  first 
place  retarded  by  gravity  in  its  ascent,  and  the  accelera- 
tion afterwards  by  gravity  being  less  than  this  previous 
retardation,  it  consequently  does  not  go  so  far,  or  has  not 
such  a wide  range,  as  if  projected  from  a height.  Skilful 
generals,  in  bombarding  towns  at  a safe  distance,  take  ad- 
vantage of  this  law  of  projectiles. 


219.  Give  examples  of  curvilinear  direction. 

220.  What  law  of  motion  is  shown  by  cannon  balls  1 

221.  Why  this  similarity  of  time  1 


LAWS  OF  PROJECTILES. 


S4 


We  are  now  prepared  for  the  consideration  of  one  of 
the  most  important  principles  in  Dynamics,  namely,  the 
law  of  motion  which  governs  a body  after  receiving  a pro- 
jectile impulse. 

243.  A projectile  exhibits  a composition  of  motion, 
namely,  a horizontal  motion  forward,  when  thrown  in  that 
direction,  produced  by  the  impressed  force  ; and  a descend- 
ing motion,  produced  by  gravity,  or  the  earth’s  attraction. 
These  two  motions  are  unequal;  they  are  not  at  the  same 
velocity.  The  horizontal  motion  is  uniform,  while  the 
descending  motion,  according  to  the  law  of  gravitation  in 
relation  to  falling  bodies  (see  170),  is  accelerated.  The 
consequence  is,  that  the  projectile,  as  already  mentioned, 
pursues  a curved  line  of  direction,  the  convex  side  of  the 
curve  being  uppermost. 

244.  The  degree  of  curvature  of  the  h'ne  of  motion 
depends  on  the  amount  of  the  original  projectile  force. 
The  law  is,  the  greater  the  projectile  force,  or  the  greater 
the  original  velocity  of  the  object,  so  is  the  sweep  of  the 
curve  proportionally  greater. 

245.  Let  us  suppose  that  the  projectile  force  is  sufficient 
to  carry  a cannon  ball  ten  miles;  this  will  give  a very 
wide  curve,  allowing  that  the  ball  is  shot  from  a lofty  situa- 
tion. But  let  us  add  to  the  projectile  force,  and  send  the 
ball  double  the  distance,  and  the  curve  is  now  exceedingly 
wide.  If  we  in  this  manner  go  on  adding  to  the  projec- 
tile force,  vve  at  length  give  the  ball  such  a moial  force 
that  it  will  go  quite  round  the  world;  instead  of  describing 
portions  of  curves,  it  will  describe  a whole  circle. 

246.  This  conducts  us  to  a most  extensive  result.  We 
have  at  once  placed  before  us  a reason  why  the  planetary 
bodies  should  have  assumed  curvilinear  paths  in  relation 
to  the  sun.  The  original  projectile  force  which  they  re- 
ceived, in  connection  with  the  force  of  gravitation,  has 
obliged  them  to  pursue  curved  lines  in  their  motion  ; and 
once  being  disengaged,  they  have,  by  a balance  of  centri- 


222.  What  law  of  projectiles  is  useful  in  military  operations  ? 

223.  What  of  the  compound  motion  of  projectiles  ? 

224.  How  is  this  law  of  projectiles  illustrated  ? 

225.  What  important  bearing  has  this  upon  astronomy  ? 


ACTION  AND  REACTION. 


85 


fugal  and  centripetal  forces,  continued  to  travel  in  circular, 
or,  properly  speaking,  elliptical  orbits — the  ellipticity  being 
caused  by  a want  of  exact  uniformity  between  the  forces 
which  affect  them. 

A calculation  of  these  forces  belongs  properly  to  Mathe- 
matics, and  will  engage  our  attention  when  treating  of 
Astronomy. 

ACTION  AND  REACTION. 

We  proceed  to  a consideration  of  the  first  clause  in  the 
third  proposition  of  Newton — “Action  must  always  be 
equal  and  contrary  to  reaction.” 

247.  Action  is  the  impression  of  force.  A blow  is  action  ; 
pressure  is  action.  Reaction  is  resistance  ; but  the  word 
resistance  does  not  fully  convey  the  meaning  of  reaction, 
which  properly  signifies  the  action  of  striking  or  pressing 
back,  even  although  the  body  struck  or  pressed  upon  do 
not  move. 

' 248.  When  a man  strikes  a hammer  upon  a fixed  stone, 
the  stone  strikes  the  hammer  at  the  moment  of  contact  as 
much  as  the  hammer  strikes  it.  But  if  the  stone  be  not 
fixed,  and  be  liable  to  be  easily  upset,  then  its  reaction  is 
less,  and  it  acquires  a momentum.  When  a boy  throws 
his  ball  against  the  wall  of  a house,  the  wall  reacts  on  the 
ball,  and  causes  it  to  rebound  ; but  if  the  boy  throw  his 
ball  at  a pane  of  glass  with  the  same  force,  the  glass,  having 
the  power  to  resist  only  a portion  of  the  force,  gives  way 
before  it.  In  this  case,  if  we  suppose  the  ball  to  possess 
the  action  or  force  of  4,  and  the  glass  to  possess  the  reac- 
tion of  2,  the  ball  in  passing  through  the  glass  loses  2 in 
its  force,  and  retains  the  remaining  2.  If  it  then  came 
against  another  pane  possessing  a reactive  power  of  2, 
it  would  not  break  the  glass,  and,  its  force  being  now  spent, 
it  would  fall  to  the  ground.  Thus,  “ action  and  reaction 
are  equal.” 

249.  A story  is  told  of  a person  who,  from  his  know- 
ledge of  the  law  of  action  and  reaction,  betted  that  he 

226.  Define  action  and  reaction,  and  their  relation. 

227.  What  illustra'ions  are  cited  ? 

228.  What  examples  in  proof  are  given  ? 


86 


ACTION  AND  REACTION. 


would  lie  down  on  the  ground  and  allow  an  anvil  to  be 
placed  upon  his  breast,  and  that  any  one  might  strike  the 
anvil  with  as  much  force  as  he  was  pleased  to  exert.  In 
this  case,  the  person  who  made  the  offer  was  quite  safe, 
provided  he  could  support  the  weight  of  the  anvil  ; for  if 
a blow  were  given  with  the  utmost  force  by  a comparatively 
light  body,  as  a hammer,  though  it  would  communicate 
nearly  double  its  momentum  to  the  anvil,  yet  the  anvil, 
being  so  heavy,  would  acquire  so  small  a velocity  that  the 
shock  given  to  the  person  would  be  insensible.  Were 
a freestone  of  the  same  weight  as  the  anvil  used,  it  would 
give  a still  less  shock,  for  the  action  and  reaction  of  per- 
fectly elastic  bodies  are  twice  as  great  as  that  of  inelastic 
bodies.  Iron  has  more  elasticity  than  stone. 

250.  It  is  by  reaction  acting  contrary  or  in  opposition 
to  action,  that  the  movements  of  living  objects  are  rendered 
effectual.  When  we  walk  on  the  ground,  the  ground 
resists  the  pressure,  and  we  feel  ourselves  steadied.  A 
bird  in  flying  pushes  itself  onward  by  the  flapping  of  its 
wings  against  the  partially  resisting  medium  of  the  atmo- 
sphere. The  partially  resisting  force  of  water,  in  the  same 
manner,  allows  a fish  to  propel  itself  by  its  'tail  and  fins. 
A sailor  in  rowing  a boat  causes  the  oars  to  push  against 
the  water,  and,  the  water  partially  resisting  the  force, 
motion  is  communicated  to  the  boat.  In  pushing  a boat 
from  the  shore,  the  firm  ground  has  such  a power  of  reac- 
tion, that  we  are  able  to  give  the  boat  much  greater  mo- 
mentum than  if  we  pushed  only  against  water.  If  we 
go  into  the  boat,  and  try  to  move  it,  by  merely  pressing 
against  some  part  of  its  fabric,  no  motion  whatever  is  pro- 
duced, for  the  action  and  reaction  are  equal.  The  whole 
force  employed  must  be  rendered  greater  than  the  reaction, 
otherwise  no  motion  can  be  communicated  to  the  body. 

251.  When  two  bodies  come  into  collision  with  each 
other,  as  in  case  of  two  bodies  moving  in  a straight  line, 
but  opposite  course  to  each  other,  the  law  of  action  and 
reaction  being  equal,  will  not  be  clearly  illustrated,  unless 
the  collision  be  in  the  direction  of  the  centre  of  gravity  or 


229.  What  of  the  movements  of  living  objects  ? 


MOTION  IN  ELASTIC  BODIES. 


87 


inertia  of  the  two — in  common  language,  unless  the  blow 
be  fair.  The  centre  of  gravity,  in  cases  of  this  kind,  is 
called  the  centre  of  action,  or  percussion.  For  example, 
when  we  strike  a ball  with  a club,  fairly  against  its  side 
opposite  to  its  centre  of  gravity,  it  is  impelled  to  a con- 
siderable distance  ; but  if  we  strike  it  above  this  central 
point,  a part  of'the  force  is  expended  in  vain,  or  lost,  and 
the  ball  moves  but  a comparatively  short  distance.  Expe- 
rience has  demonstrated  that  the  centre  of  action  in  ham- 
mers should  be  in  the  head  or  striking  part ; and,  there- 
fore, in  striking  with  these  instruments,  the  blow  may  be 
given  with  every  advantage.  But  when  an  attempt  is 
made  to  strike  with  an  object  in  which  the  centre  of  action 
is  at  a place  short  of  its  extreme  point,  for  instance,  a com- 
mon iron  poker,  a part  of  the  action  is  expended  towards 
the  hand  of  the  person  who  strikes,  and  he  feels  a dis- 
agreeable jarring  sensation  in  his  arm. 

252.  This  definition  of  the  centre  of  action  applies  only 
to  the  motion  of  bodies  in  a straight  line.  In  the  case  of 
revolving  bodies,  the.  centre  of  action  or  percussion  is  a 
point  in  it,  to  which  if  an  immovable  obstacle  be  applied, 
the  body  will  remain  at  rest  without  any  tendency  to  move 
in  any  direction,  and  the  axis  will  receive  no  shock.  In 
straight  rods,  or  bodies  of  any  form,  suspended  as  pendu- 
lums, the  centre  of  oscillation  is  the  same  as  the  centre  of 
action  in  revolving  bodies. 

MOTION  IN  ELASTIC  BODIES. 

252.  In  reference  to  the  effects  of  collision,  bodies  are 
divided  into  three  classes — hard,  soft,  and  elastic.  A hard 
body  is  one  that  suffers  no  change  of  form  by  the  action 
of  any  force.  A soft  body  is  one  that  undergoes  a change 
of  form  by  this  means.  An  elastic  body  suffers  a momen- 
tary change  of  form  by  the  action  of  any  force  impressed 
upon  it,  and  immediately  springs  back,  or  recovers  its 
original  form.  The  first  two  classes  are  styled  inelastic 
bodies. 

230.  What  of  the  centre  of  percussion  ? 

231.  What  difference  in  the  kind  of  motion? 

232.  Define  inelastic  bodies. 


88 


REFLECTED  MOTION. 


254.  If  two  equal  inelastic  bodies  bp  moving  with  equal 
velocities  in  opposite  directions,  and  come  in  collision, 
each  will  destroy  the  onward  motion  of  the  other,  and, 
consequently,  both  will  be  reduced  to  a state  of  rest. 

255.  If  there  be  any  elasticity  in  the  bodies,  they  will, 
according  to  their  degree  of  elasticity,  rebound  from  each 
other,  and  a positive  process  of  reaction  will  be  exhibited. 
By  this  means  there  will  be  at  once  a counteraction  and 
transmission  of  force.  As  above  stated,  when  the  bodies 
are  perfectly  elastic,  the  action  and  reaction  are  double 
those  of  inelastic  bodies. 

256.  An  example  of  the  transmission  of  force  or  motion 
from  one  body  to  another,  while  the  transmitting  bodies 
remain  at  rest  from  their  mutual  counteraction  of  the  force 
communicated,  may  be  seen  in  the  case  of  a row  of  bil- 
liard balls,  which  possess  a certain  elasticity.  Place  six 
billiard  balls  in  a row  on  a smooth  plane,  and  let  them  be 
all  pretty  close  to  each  other,  or  even  in  contact.  Then 
give  a smart  blow  to  the  first  bail,  or,  as  we  may  call  it, 
No.  1 ; it  will  instantly  strike  against  No.  2,  which  will 

Fis-  9-  communicate  the  force  to  No.  3,  and  from  3 it 
, will  be  given  to  4,  and  from  4 to  5,  and  from 
5 to  6.  None  of  the  balls,  however,  will  sen- 
sibly move  from  the  spot  in  which  it  rests, 
except  the  last  of  the  row,  which,  having  no 
ball  to  impinge  upon,  will  roll  away,  and  thus 
expend  the  force  communicated  by  the  blow 
upon  No.  1.  An  experiment  of  this  kind  is 
generally  performed  upon  a number  of  elastic  balls  of  a 
small  size,  suspended  in  a row  by  threads,  as  in  figure  9, 
in  which  case  there  is  no  friction  to  interrupt  the  process 
of  action  and  reaction. 


666 


REFLECTED  MOTION. 


257.  A body  projected  by  a single  force  proceeds  in  a 
straight  line  till  a new  force  act  upon  it,  and  send  it  on  a 


233.  Name  the  experiment  with  the  billiard  halls. 

234.  What  of  reflected  motion,  with  examples? 


REFLECTED  MOTION. 


80 


row  line  of  direction  When  amoving  body  is  thus  im- 
pelled into  a new  line  by  striking  against  some  body,  its 
motion  is  said  to  be  reflec’ed. 

258.  Examples  of  reflected  motion  are  very  common; 
as,  for  instance,  when  a rolling  ball  encounters  an  opposing 
stone  in  its  path,  in  which  case  it  flies  off  obliquely  in  a 
new  direction  ; when  we  throw  a thin  piece  of  slate  along 
the  surface  of  a river,  and  make  it  skip  from  point  to 
point ; or  when  an  apple,  in  falling  from  a tree,  touches  a 
lower  branch  in  its  descent,  and  rebounds  in  a slanting 
direction  to  the  ground. 

256.  It  is  found  by  experiments,  that  moving  bodies 
observe  certain  laws  in  respect  to  the  line  of  direction 
they  pursue  in  rebounding  or  being  reflected  from  any 
impediment  with  which  they  happen  to  come  in  contact. 

260.  In  the  accompanying  cut,  figure  10,  the  line  A B is 

a level  marble  slab.  C is 

c an  ivory  ball,  which,  being 
thrown  towards  the  slab  in 
the  direction  of  C E,  is 
B reflected  in  the  direction 
ED.  Thus,  the  two  angles 
F and  G are  exactly  equal;  and  it  is. demonstrated, that 
a perfectly  elastic  ball  striking  a smooth  wall  or  floor  makes 
the  same  angle  in  leaving  the  point  where  it  strikes  that 
it  does  in  approaching  it. 

261.  Whatever  be  the  angle  at  which  the  ball  strikes 
the  smooth  fixed  surface,  the  same  rule  will  be  observed  to 

be  followed.  This  is  exem- 
p ified  in  figure  11.  If  the 
ball  be  dropped  perpendicu- 
larly from  L to  K,  it  will  re- 
bound and  return  to  L.  If 
sent  in  the  line  H K,  it  will 
rebound  or  be  reflected  to  I. 
The  angle  which  a ball  makes 
with  the  perpendicular  line  in  goingfrom  H to  K,  is  call  d 


235.  Explain  the  diagram. 

236.  Explain  the  diagrams,  and  angle  ot  incidence. 


90  COMPOSITION  OF  MOTION  AND  FORCES. 

the  angle  of  inci  fence;  and  the  angle  which  it  makes  in 
rebounding  from  the  point  at  K to  I,  is  called  the  angle 
of  reflection.  These  angles  are  always  equal. 

262.  A calculation  of  the  angles  of  reflected  motion  is 
necessary  in  the  case  of  presenting  a shield  or  other  object 
to  ward  off  a missile  or  blow  from  the  person.  If  the 
angle  be  too  acute,  that  is,  if  the  blow  be  too  point-blank, 
the  shielding  object  may  be  damaged,  or  perhaps  destroyed ; 
while,  if  the  angle  be  obtuse,  the  object  which  gives  the 
blow  will  slide  off  harmlessly.  In  playing  at  the  game  of 
billiards,  the  greatest  exactness  is  required  in  the  calcula- 
tion of  the  forces  and  their  directions  according  to  the 
principles  of  reflected  motion  ; and  a similar  kind  of  skill 
is  required  by  those  who  handle  the  bat  in  the  game  of 
cricket. 

THE  LAWS  OF  MOTION  CONTINUED. 

COMPOSITION  OF  MOTION  AND  FORCES. 

263.  Hitherto  we  have  spoken  only  of  the  motion  of  a 
body  as  produced  by  a single  impulsive  force,  and  turned 
aside  or  reflected  by  another  force  acting  upon  it ; we  have 
now  to  consider  the  subject  of  compound  motion  and  force, 
or  motion  and  force  produced -by  two  or  more  forces  acting 
on  a body  in  different  directions  at  the  same  time. 

264.  If  two  or  more  forces  act  on  a given  point  of  a 
body,  at  certain  angles,  a single  force  may  be  found  which 
would  produce  the  same  effect.  This  single  force  is  tech- 
nically called  the  resultant  or  equivalent.  For  instance, 
a wind  blowing  from  the  north-west,  and  a current  setting 
from  the  north-east,  both  acting  on  a ship  and  tending  to 
carry  it  with  equal  velocities  in  their  own  directions,  the 
ship  will  be  found  to  move  in  an  intermediate  direction,  as 
if  it  were  acted  on  by  a single  force,  like  a breeze,  from 
due  north. 

It  is  usual,  in  treating  of  combinations  of  mechanical 
forces,  to  represent  them  by  diagrams,  the  various  lines  of 
which  are  significant  of  the  quantity  or  intensity  of  the 


237.  What  use  is  the  calculation  of  the  angles  of  reflection? 

238.  What  of  compound  forces,  and  the  resultant? 


COMPOSITION  OF  FORCES. 


SI 


forces,  of  the  directions  in  which  they  act,  and  of  the 
effects  produced  by  them.  This  explains  the  reason  for 
illustrating  the  action  of  forces  by  the  following  figures: 

265.  In  figure  12,  we  have  an  example  of  motion  pro- 

Fig.12.  duced  by  two  forces  in  different 

directions  acting  on  a body.  . A is 
a ball,  which,  having  received  a 
c blow  at  B,  is  proceeding  onward  to 
C.  At  the  point  A,  while  on  its 
course,  it  receives  a blow  equal  to 
the  former,  which  second  blow 
would  have  been  alone  capable  of 
carrying  it  to  E in  the  same  time 
f that  the  first  blow  would  have  car- 
ried it  to  C.  This  new  force,  by  changing  the  direc- 
tion of  the  original  motion,  causes  the  ball  to  move  in  a 
line  towards  F,  and  the  effect  is  the  same  as  if  the  ball  had 
been  at  first  sent  in  the  direction  of  A F by  a single  force. 
Practically- it  would  be  difficult  to  regulate  blows  with  such 
nicety  as  to  produce  this  line  of  motion,  but  in  the  theory 
of  forces  the  law  is  as  it  has  been  stated.  The  line  A F 
in  the  figure  here  drawn  is  termed  the  diagonal  of  (he 
square. 

266.  Should  the  constituent  forces  be  of  different  mag- 
nitudes, then  the  figure  described  maybe  a parallelogram, 
or  oblong,  as  in  the  annexed  cut,  fig.  13.  The  force  here, 
in  the  direction  A B,  is  double  that  of  the  cross  force  C D, 

Fig.  is.  by  which  means  the  ball  describes 

a diagonal  line  to  F,  and  so  forms 
a parallelogram,  when  we  draw 
all  the  lines  connected  with  the 
experiment.  The  parallelogram 
thus  formed  is  called  the  paral- 
lelogram of  forces.  The  two 
given  forces  acting  in  the  direc- 
tions E B,  E D,  are  called  components,  and  the  single 
force  in  the  direction  E F is  the  resultant.  The  process 


239.  Explain  the  first  diagram,  and  the  diagonal  of  the  square. 

240.  Describe  the  second,  and  the  italicised  terms. 


92 


COMPOSITION  OF  FORCES. 


of  finding  a single  force  equivalent  to  two  or  more  forces, 
is  called  the  composition  of  forces. 

267.  The  process  of  finding  forces  which  will  produce  a 
motion  equal  to  that  of  a single  force,  is  called  the  resolu- 
tion of  forces. 

The  following  are  examples  of  the  resolution  of  forces  : — 

268.  If  a boat  DEM  floating  on  a river  be  pressed 
downwards  in  the  line  M C by  a current,  two  forces  P and 

F'g- 14.  _ Q,,  acting  in  the  di- 

rections M P,  M Q., 
may  be  found  that 
will  counteract  the 


R C, 

D 

M / 
-U-  =5^-- 

R' 

E 

rent,  and  keep  the 
boat  stationary.  F or, 
make  M C to  repre- 
Q sent  R,  the  force  of 

the  current,  and  make  MC'  equal  to  M C,  and  find  M A 
and  M B as  before,  they  will  respectively  represent  P and 
Q,.  If  two  men,  therefore,  pull  two  ropes  in  the  directions 
M P,  M Q.,  with  forces  denoted  by  M A,  M B,  they  would 
keep  the  boat  at  rest.  If  the  ropes  be  tied  to  two  posts  at 
P and  Q.,  the  forces  M A,  M B,  will  represent  their  reac- 
tions. 

269.  Let  HM  be  a canal  boat,  M P the  rope  by  which 
it  is  drawn  by  a horse  attached  to  it  at  P.  Thy  force  of 

the  draught  being 
denoted  by  M P,  it 
may  be  resolved  into 
M A and  M B,  of 
which  only  M A is 
effective  in  drawing 


Fig-.  15. 


D 'sFl 


the  boat  forward ; the  other  force  M B tends  to  turn  the 
head  of  the  boat  in  the  direction  M B.  This  last  force  must 
therefore  be  counteracted,  which  is  effected  by  means  of 
the  helm  H E turned  to  an  oblique  position.  When  the 
boat  is  in  motion,  the  water,  being  at  rest,  produces  a re- 


241.  What  is  the  first  diagram  ? 
24 Q.  Explain  the  record. 


composition  of  forces. 


93 


sistance  or  pressure  against  the  helm.  If  C D denote  the 
resistance,  it  may  be  resolved  into  H D and  H C,  of  which 
H D produces  no  effect  on  the  helm ; therefore  C H is  the 
only  effective  pressure.  Again,  C H may  be  resolved  into 
C F and  F H,  the  latter  of  which  tends  to  turn  the  stern 
of  the  boat  in  the  direction  F H,  and  thus  counteracts  the 
force  M B,  by  tending  to  turn  the  boat  round  in  an  oppo- 
site direction ; and  the  part  C F tends  to  move  the  boat 
backwards,  and  thus,  counteracting  a part  of  the  force  M A, 
it  retards  the  progress  of  the  vessel.  The  two  forces  F H, 
M B,  would  move  the  boat  sideways,  or  laterally,  to  the 
side  of  the  canal ; but  this  can  be  prevented  by  giving  the 
helm  a little  more  obliquity,  for,  from  the  length  and  shape 
of  the  vessel,  it  is  much  more  easily  moved  in  'the  direc- 
tion of  its  length  than  of  its  breadth. 

270.  Let  TP  be  a ship,  S L its  sail,  W A the  direction 
of  the  wind  and  its  pressure  on  the  sail.  W A can  be  re- 
solved into  A B perpendicular  to  the  sail,  and  B W 
parallel  to  it,  the  latter  of  which  has  no  effect  in  pressing 
on  the  sail ; therefore  A B is  the  effective  pressure  on  the 
sail.  Were  the  vessel  round,  it  would  move  in  the  direc- 
tion B A.  Let  B A be  resolved 
into  C A and  B C,  the  former  C A 
acting  in  the  direction  of  the  keel 
or  length  of  the  vessel,  or  in  the 
direction  C'A,  and  the  latter  per- 
pendicular to  it,  or  in  the  direction 
of  the  breadth.  The  former  pres- 
sure C A is  the  only  pressure  that 

moves  the  vessel  forward,  the  other  BC  makes  it  move 
sideways.  From  the  form  of  the  vessel,  however,  this  lat- 
ter force  BC  produces  comparatively  little  lateral  motion ; 
any  that  it  does  occasion,  is  called  leeway.  By  turning 
the  helm,  the  vessel  may  be  made  to  turn  round  in  any 
direction  by  the  pressure  of  the  water  upon  it,  if  the  vessel 
has  also  at  the  same  time  progressive  motion. 

271.  The  suspension  of  a kite  in  the  air  is  another 


243.  Explain  the  diagram. 


94 


COMMON  MOTION. 


interesting'  illustration  of  the  eff  ct  of  the  pressure  of  a 
current  of  air,  the  explanation  of  which  belongs  to  Pneu- 
matics. 

THE  LAWS  OF  MOTION  CONCLUDED. 

COMMON  MOTION. 

272.  Motion,  as  has  been  stated  (154),  is  called  common, 
when  participated  in  by  two  or  more  bodies.  Thus,  all 
things  on  the  earth,  including  the  atmosphere,  have  a mo- 
tion in  common  with  the  earth  ; a person  riding  in  a chaise 
has  a motion  in  common  with  the  chaise  ; a person  in  a mov- 
ing vessel  at  sea  has  a motion  in  common  with  the  vessel. 

For  convenience,  we  shall,  in  treating  of  this  branch  of 
our  subject,  use  the  terms  larger  and  smaller  body — the 
larger  being  understood  to  be  the  body  on  which  the  force 
to  produce  motion  is  immediately  impressed,  and  the 
smaller  being  the  body  which  is  carried  along  by  the  body 
which  has  received  this  impression  of  force. 

273.  A large  body  is  in  motion  ; it  is  moving  in  a cer- 
tain direction,  at  a certain  velocity  ; every  thing  on  it,  or 
small  body  connected  with  it,  partakes  in  its  motion,  and 
has  a tendency  to  proceed  in  the  same  direction,  and  at 
the  same  velocity. 

274.  It  appears  strange  that  there  should  be  a com- 
munication of  motion  from  the  larger  body  to  the 
smaller,  without  the  immediate  intervention  of  impressed 
force  on  the  smaller  ; but  a little  examination  shows  that 
such  must  necessarily  be  the  case.  The  larger  body  has 
received  the  impulse  to  move,  and  this  impulse  is  trans- 
mitted through  the  whole  mass  of  the  body,  including  all 
the  small  objects  on  its  surface,  and  those  which  are  any 
way  connected  with  it  in  its  propulsion.  When  a man  is 
walking  on  the  deck  of  a ship  which  is  moving  at  the  rate 
of  ten  miles  an  hour,  he  perhaps  imagines  that  he  has  no 
more  motion  than  if  he  were  walking  on  the  solid  ground. 
But  it  would  be  incorrect  for  him  to  think  so.  His  body. 


244.  What  of  common  motion,  with  examples  ? 

245.  How  is  it  accounted  for  ? 


COMMON  MOTION. 


95 


' and  every  thing  about  his  person,  have  received  an  im- 
pulse from  the  vessel ; he  possesses  a velocity  of  ten  miles 
an  hour  as  much  as  the  planks  of  the  vessel  do ; and  this 
onward  motion  he  cannot  divest  himself  of,  as  long  as  the 
ship  continues  to  move  at  this  rate  of  speed,  or  as  long  as 
he  continues  in  connection  with  it. 

275.  On  account  of  this  participation  of  motion  in  ail 
bodies  moving  in  connected  masses,  it  is  observed  that  all 
objects  whatever  keep  their  proper  places  in  or  about  the 
large  moving  bodies  with  which  they  are  in  contact,  and 
hence  no  confusion  takes  place  in  the  relative  situation 
of  objects  on  the  earth  by  its  motion.  For  example,  when 
we  leap  from  the  ground,  the  earth  does  not  slip  away 
from  below  us  ; if  we  ascend  in  a straight  line  of  direction, 
we  fall  down  exactly  upon  the  same  spot  whence  we  arose. 
When  a man  falls  from  the  top  of  a mast  of  a moving  ves- 
sel, he  falls  upon  the  deck  upon  a spot  directly  under  the 
point  whence  he  fell ; the  vessel  does  not  leave  him. 
When  we  are  sitting  in  the  cabin  of  a moving  vessel,  and 
let  a small  object  drop  from  our  hand  to  the  floor,  it  falls 
on  a point  on  the  floor  immediately  below,  the  same  as  if 
it  had  been  dropped  in  a house  on  solid  ground  ; the  floor 
does  not  leave  it  behind.  When  we  are  sitting  in  a 
rapidly  moving  coach,  and,  in  a similar  manner,  let  an 
object  fall,  it  descends  in  the  same  manner  to  the  bottom 
of  the  coach.  The  reason  for  these  phenomena  is  that 
already  mentioned — the  small  objects  possess  a motion 
derived  from  the  larger ; this  common  motion,  or  motal 
inertia , as  some  authors  call  it,  is  retained  by  the  small 
objects  during  their  descent,  so  that,  while  descending, 
they  are  also  going  forward  ; in  other  words,  they  display 
a composition  of  motion — a horizontal  motion  and  a de- 
scending perpendicular  motion. 

276.  One  of  the  most  beautiful  examples  of  common 
motion,  is  that  which  is  exhibited  by  an  equestrian  stand- 
ing on  a horse  which  is  running  round  a circle,  while  he 
it  the  same  time  throws  oranges  from  his  hand  and  catcfus 
’mm  in  their  descent.  Notwithstanding  his  rapid  motion, 


246.  Name  the  familiar  examples  of  this  motion. 


96 


COMMON  MOTION. 


the  oranges  which  anj  thrown  into  the  air  do  not  fall  be- 
hind  ; they  return  regularly  to  his  hand.  To  counteract 
centrifugal  force,  he  leans  greatly  inward  ; but  this  does 
not  alter  the  law  of  motal  inertia,  which  causes  the  oranges 
to  return.  He  throws  them  almost  sidewise  in  an  inward 
slanting  direction,  and  yet  they  come  readily  back  to  him. 
The  reason  for  these  phenomena  is.  that  the  oranges  par- 
ticipate in  the  forces  by  which  he  himself  is  impelled  and 
sustained. 

277.  Small  bodies  which  have  derived  a motal  inertia 
from  a larger,  continue  to  possess  this  motal  inertia,  after 
leaving  the  larger,  untl  they  meet  with  some  new  impres- 
sion of  force  sufficient  to  alter  their  condition.  If  they 
were  not  pulled  to  the  earth  by  attraction,  and  were  not 
opposed  by  the  atmosphere,  they  would  go  on  moving  in 
a straight  line  for  ever. 

27S.  When  we  drop  a ball  from  the  window  of  a moving 
coach,  it  continues  to  go  forward,  as  if  it  were  still  in  the 
coach,  till  it  meet  the  ground,  when  it  is  stopped  ; thus, 
its  motal  inertia  :s  destroyed.  If  we  attempt  to  leap  from 
a moving  body,  such  as  a coach  or  a boat,  we  continue  to 
possess  the  motion  which  we  previously  had  until  we 
touch  the  earth,  when  we  receive  a shock  by  the  destruc- 
tion of  our  motal  inertia.  But  if  we  leap  from  one  moving 
body  to  another  moving  body  which  is  going  near  it,  on 
the  same  level,  in  the  same  direction,  and  at  the  same  ve- 
locity, we  sustain  no  shock,  because  the  body  upon  which 
we  leap  possesses  the  same  condition  of  motion  as  that 
which  we  possess. 

279.  When  a man  standing  on  the  ground  shoots  at  a 
bird  on  the  wing,  he  requires  to  follow  its  motion  by  keep- 
ing his  gun  moving  when  presented  at  it ; but  if  he  be 
standing  on  the  deck  of  a ship  sailing  at  the  rate  of  ten 
miles  an  hour,  and  point  his  gun  at  a bird  flying  in  the 
same  direction  and  at  the  same  velocity  as  the  ship,  then 
he  is  placed  in  the  same  condition  as  the  bird ; he  does 
not  require  to  move  his  gun,  as  if  following  the  bird.  In 


247.  Repeat  and  explain  the  illustrations  cited. 

248.  Describe  the  uses  of  understanding  this  law. 


COMMON  MOTION. 


9/ 


taking  aim  at  a bird  on  the  wing  from  the  solid  ground,  it 
requires  considerabJe  skill  to  prevent  the  shot  from  pro- 
ceeding to  a point  behind  the  bird,  because  the  shot  is 
entirely  destitute  of  rnotal  inertia  on  being  fired,  unless  it 
be  previously  put  in  motion.  But  a bullet  on  leaving  a 
gun  which  is  moving  at  the  same  rate  as  the  bird,  and  in 
the  same  direction,  keeps  going  on  in  the  direction  of  the 
bird,  because  it  retains  the  motion  it  had  in  common  with 
the  gun.  The  bullet  in  this  case  does  not  go  in  the 
direction  of  the  gun,  but  obliquely,  so  as  to  keep  up  with 
the  motion  of  the  bird,  so  that  the  same  effect  is  produced 
as  if  the  shot  had  been  fired  from  a fixed  gun  on  land  to  a 
fixed  point  in  the  air  in  advance  of  the  bird.  Should  the 
bullet  be  fired  from  a gun  in  a moving  vessel,  for  instance 
a ship  sailing  westward  to  a fixed  point  on  land,  then  a 
certain  allowance  must  be  made  for  the  motal  inertia  of 
the  bullet ; it  must  be  fired  a little  eastward,  and  the  motal 
inertia  will  carry  it  westward  to  the  object. 

280.  Objects  falling  from  bodies  moving  in  an  onward 
direction  to  those  which  are  at  rest,  are  regulated  by  the 
same  law  that  governs  projectiles.  The  falling  objects,  as 
formerly  mentioned,  are  affected  by  two  motions — one  in 
a horizontal  and  the  other  in  a descending  direction. 
When  these  motions  are  unequal,  the  falling  body  de- 
scribes a curve  in  its  descent,  the  convex  side  of  the  curve 
being  uppermost.  Thus,  motal  inertia  and  the  motion  pro- 
duced by  projectile  impulse  are  the  same  thing  ; and  hence, 
powerful  centrifugal  force  in  the  sun,  sufficient  to  disen- 
gage a portion  of  its  mass,  would  be  equivalent  to  a projec- 
tile impulse  from  it  as  a fixed  body. 

281.  In  consequence  of  the  general  participation  of 
common  motion  in  all  things  connected  with  a moving 
body,  there  can  be  no  consciousness  of  motion  in  the  living 
beings  carried  about  by  it,  provided  the  motion  be  perfectly 
smooth,  and  there  be  no  means  of  observing  bodies  which 
are  at  rest.  Thus,  on  account  of  our  possessing  a motion 
in  common  with  the  earth,  which  moves  with  perfect 
smoothness,  we  can  neither  see  nor  feel  the  earth  moving. 


249.  When  are  we  consci  ms  of  p ir'icipaiing  in  this  motion  ? 


98  CONCLUSION  OF  LAWS  OF  MOTION. 

We,  however,  see  the  sun,  which  seems  to  us  to  be  in 
motion  in  reference  to  the  earth,  but  which,  by  various 
means,  we  know  to  be  at  rest ; and  hence  we  are  assured 
of  the  earth’s  diurnal  rotation  on  its  axis,  and  its  annual  or 
planetary  motion  round  the  sun.  In  the  same  manner,  a 
person  sitting  in  the  cabin  of  a smooth-sailing  ship,  and 
not  looking  out  at  the  windows,  cannot,  by  his  mere  sen- 
sations, tell  that  the  vessel  is  moving  ; but  if  he  look  at  the 
shore,  which  is  at  rest,  he  is  immediately  sensible  of  the 
progressive  motion  of  the  vessel. 

2&2.  In  looking  from  a moving  body,  as  from  the  earth 
to  the  sun,  from  a ship  to  the  shore,  or  from  a coach  to 
objects  on  the  wayside,  a delusive  feeling  prevails  that  it 
is  not  the  body  you  are  upon,  but  the  body  which  is  at 
rest,  that  is  ready  moving — going  in  a direction  contrary 
to  that  of  the  body  you  are  connected  with.  This  is  in 
consequence  of  our  possession  of  motion  in  common  with 
the  moving  body.  We  are  under  an  influence,  or  in  a 
condition,  that  renders  us  incapable  of  seeing  our  own 
motion : and,  hence,  the  error  which  the  sense  of  vision 
leads  us  to  commit,  is  left  to  be  rectified  by  an  exertion  of 
the  understanding. 

The  subject  of  the  next  Book  is  Mechanics,  or  a treatise 
on  Mechanical  Powers  and  Machinery,  being  the  ap 
plication  of  the  laws  above  demonstrated  to  contrivances 
for  lessening  and  aiding  human  labour. 

250.  Why  are  we  not  so,  and  when  1 

251.  To  what  mistakes  are  we  liable,  and  why  ? 


THE  END. 


STEREOTYPED  BY  L.  JOHNSON  AND  CO. 
PHILADELPHIA. 


ELEMENTS 

OF 

NATURAL  PHILOSOPHY. 


PART  II. 

MECHANICS. 


CHAMBERS’  EDUCATIONAL  COURSE. 


. 

- 


■ 


i 


INTRODUCTORY  OBSERVATIONS 


BY 

THE  AMERICAN  EDITOR. 


This  second  book  of  Natural  Philosophy  is  designed  to  fol- 
low the  work  on  Matter  and  Motion,  which  is  introductory  to 
practical  Mechanics,  and  should  first  be  made  familiar  to  both 
the  teacher  and  scholar.  The  catechetical  questions  upon 
every  page  of  both  these  volumes  are  designed  to  furnish  such 
an  analysis  of  every  topic  as  shall  render  the  acquisition  of 
the  elements  of  these  departments  of  science  so  easy  that 
none  may  be  deterred  from  their  cultivation  ; and  if  the  sug- 
gestions of  the  preface  be  acted  upon,  and  the  learners  be  en- 
couraged to  construct,  with  their  own  hands,  simple  and  rude 
apparatus,  which  shall  illustrate  the  principles  taught,  no 
study  will  be  more  delightful  to  children  than  the  departments 
of  nature  and  art  to  which  these  sciences  introduce  them. 

Nothing  can  be  more  gratifying  to  the  philanthropist,  than 
to  witness  the  march  of  mind,  characteristic  of  the  present 
age,  as  exemplified  in  the  diffusion  of  scientific  knowledge 
among  the  masses  of  the  people,  by  the  adaptation  of  the 
teachings  of  philosophy  to  the  young  and  rising  generation. 
Instead  of  locking  up  knowledge  in  these  higher  walks  of 
science  in  cloisters  and  academic  groves,  accessible  only  to  a 
favoured  few,  the  teachings  of  philosophy  are  now  disrobed 
of  all  their  mystery,  and  by  cheap  publications  they  are  ra- 
pidly becoming  the  property  of  all. 

The  educational  series,  of  which  this  little  volume  forms  a 
part,  is  calculated  to  initiate  the  young  into  the  elements  of  all 

3 


4 


INTRODUCTORY  DBS K RVATIONS. 


the  sciences,  even  in  the  common  school.  The  poorest  chil- 
dren of  the  present  generation  may  thus  become  wiser  than 
their  parents,  and  understand  more  of  philosophy  and  science 
than  was  the  lot  of  any  in  the  previous  century,  except  those 
whom  fortune  favoured  with  wealth  and  thorough  collegiate 
training,  extending  to  adult  years,  and  even  consuming  the 
greater  part  of  life  in  the  seclusion  of  study.  And  a taste  for 
such  pursuits  being  thus  early  acquired,  and  the  habit  of  in- 
vestigation into  the  nature  and  causes  of  things  becoming,  as 
it  will,  a part  of  their  mental  constitution,  it  is  impossible  to 
predict,  or  to  limit,  the  practical  improvements  and  useful  dis- 
coveries which  will  result,  or  the  amount  of  increase  to  hu- 
man progress  and  happiness  which  this  generation  shall 
witness. 

The  admirable  “ Lectures  of  Dr.  Lardner  on  Science  and 
the  Useful  Arts,”  now  in  the  course  of  publication,  are  so 
well  adapted  to  the  popular  mind,  that  as  a sequel  to  these 
volumes,  they  cannot  fail  to  be  appreciated,  and  they  will  be 
eminently  useful  in  proportion  as  they  are  read  by  those  who 
are  trained  in  their  schools  to  estimate  the  importance  and 
necessity  of  philosophy  in  every  department  of  art,  and  in  the 
economy  of  human  life. 

Let  parents  and  teachers  then  avail  themselves  of  this  series 
and  other  kindred  publications  to  cheapen  knowledge,  and 
diffuse  it  abroad  far  and  wide  among  the  masses,  in  conform- 
ity with  the  spirit  of  the  age. 


D.  M.  R. 


PREFACE. 


The  present  Treatise,  comprehending'  Mechanics,  the  Ele- 
ments of  Practical  Machinery;  and  Moving  Forces,  forms 
the  second  department  of  Natural  Philosophy,  according  to 
the  arrangement  described  in  the  Preface  to  the  Laws  of 
Matter  and  Motion. 

A passage  of  that  preface,  as  of  general  application,  may 
appropriately  be  repeated  here: — “In  exercising  a class  in 
this  and  other  departments  of  Natural  Science,  it  will  be 
found  to  be  of  considerable  importance  to  cause  each  para- 
graph to  be  mastered  or  thoroughly  understood  before  pro- 
ceeding to  what  follows  ; for  the  whole  constitutes  a structure 
in  which  each  part  rests  on  what  has  gone  before  it.  The 
pupil  should,  also,  not  only  read,  but  be  induced  to  think  on 
the  nature  of  the  principles  which  are  unfolded,  and  led  to 
find  examples  of  their  action  in  the  every-day  concerns  of  life, 
and  the  common  phenomena  of  the  universe.”  It  is  further 
suggested,  that  pupils  should,  by  the  aid  of  small  pieces  of 
wood,  cord,  and  other  easily  procured  materials,  endeavour  to 
work  out,  with  their  own  hands,  the  various  principles  of  Me- 
chanics which  are  demonstrated  in  the  following  pages.  It  is 
believed,  that  by  no  other  means  could  these  valuable  princi- 
ples be  so  well  fixed  in  the  memory,  or  have  such  a powerful 
effect  in  cultivating  the  understanding. 

In  the  present,  as  in  the  preceding  Treatise,  very  great  pains 
have  been  taken  to  render  the  language  simple  and  intelli- 
gible, so  that  the  learner  may  find  at  least  no  technical  diffi- 
culty in  his  path.  Those  who  are  desirous  of  pursuing  the 
study  of  Dynamical  and  Mechanical  science,  beyond  the 


6 


PREFACE. 


limits  of  these  elementary  works,  and  who  possess  a know- 
ledge of  Algebraic  and  Mathematical  formulae,  are  recom- 
mended to  have  recourse  to  the  excellent  “ Treatise  of  Me- 
chanics, Theoretical  and  Practical,  by  Olinthus  Gregory 
the  “ Introduction  to  Natural  Philosophy,  bf  William  Nichol- 
son or  to  the  Treatises  of  Wood,  Leslie,  and  Whewell 
No  popular  and  comprehensive  treatise  on  the  properties  of 
matter  and  doctrines  of  forces,  excels  the  well-known  Ele- 
ments of  Physics,  by  Dr.  Neil  Arnot.  There  are  also  a few 
compendious  productions  of  American  writers  which  may  be 
consulted,  particularly  those  of  Gale,  Comstock,  and  Bigelow, 
to  which  the  Editors  have  to  acknowledge  themselves  indebted 
for  some  useful  hints.  Engineers,  mill-wrights,  and  other 
artisans,  who  require  to  make  practical  calculations,  will  find 
a small  work,  entitled  “ Burton’s  Compendium  of  Mecha- 
nics,” worthy  of  their  attention. 


CONTENTS. 


Page 

CrENEit-iL  Definitions 9 

Of  Levers 11 

First  kind  of  Lever 12 

Second  kind  of  Lever 20 

Third  kind  of  Lever 22 

Of  Compound  and  Bent  Levers 24 

Compound  Levers 24 

Bent  Levers 26 

Levers  of  oblique  action 27 

Recapitulation  of  Lever  Powers,  and  Animal  Levers 30 

Animal  Levers 31 

Of  the  Wheel  and  Axle 35 

Wheels ........  35 

Wheel  and  Axle 36 

Of  Cords  and  Pulleys 39 

Fixed  Pulleys 39 

Moveable  Pulleys 40 

Principle  of  the  Pulley  Power 42 

Combinations  of  Pulleys 43 

Practical  application  of  Pulleys 45 

Of  the  Inclined  Plane 45 

Standards  of  comparison  for  Inclinations 46 

Principle  of  the  Power  of  Inclined  Planes 47 

Rules  for  calculating  the  Power  of  Inclined  Planes.  48 

Examples... 49 

O the  Wedge 52 

Rules  for  calculating  the  Powers  of  the  Wedge 53 

Examples  of  Wedge  Powers 53 

? 


8 CONTENTS. 

Page 

Of  the  Screw 54 

Powers  of  the  Screw 55 

Rules  for  calculating  the  Powers  of  the  Screw 57 

Examples  of  Screw  Powers 59 

Mechanical  combination  and  structure 60 

Arched  Structures 64 

Elements  of  practical  Machinery 67 

Wheels 70 

Wheels  and  Pinions 70 

Practical  Examples 73 

Working  of  Toothed  Wheels 74 

Altering  the  Direction  of  Motion 74 

Bevel  Wheels 75 

Transmission  of  Power  by  Belts 75 

Shafts  and  Pulleys 77 

Changing  Velocity 78 

Preserving  regularity  of  Motion  .by  a Variable  Force  79 
Alternate  or  reciprocating  Motion — Eccentric  Wheels  80 

Oblique  action 83 

Cranks 84 

Ratchet  Wheels 84 

Engaging  and  disengaging  Machinery 85 

Practical  Machinery  continued — of  accumulating  and 

equalising  Power 85 

Accumulation 85 

Equalisation — Fly  Wheels. , . . . . 88 

Practical  Machinery  continued — Obstacles  to  Motion 89 

Friction 89 

Uses  of  Friction 93 

Resistance  of  Air  and  Water 93 

Practical  Machinery  concluded — Moving  Forces 94 

Human  Labour 95 

Horse’s  Power — Draught 98 

Water  Power 103 

Steam  Power 104 


NATURAL  PHILOSOPHY. 


MECHANICS. 


GENERAL  DEFINITIONS. 

1.  The  application  of  the  laws  of  motion  and  foices  to 
objects  in  nature  or  contrivances  in  the  arts,  forms  the 
branch  of  Natural  Philosophy  usually  treated  under  the 
head  Mechanics,  Mechanical  Powers,  or  Elements  of 
Machinery. 

2.  The  original  signification  of  the  word  machine , which 
is  the  root  of  the  various  terms  mechanic , mechanical,  and 
so  forth,  was  art,  contrivance,  or  ingenuity. 

3.  When  the  term  mechanic,  or  mechanical,  is  applied  to 
the  action  of  forces — as  mechanical  powers — it  is  meant 
that  certain  powers  are  exerted,  or  motion  produced,  by  the 
action  of  particles  or  masses  of  matter,  solid  or  fluid,  one 
upon  another.  Thus,  mechanical  action  is  applied  to  the 
action  of  forces  that  produce  no  change  in  the  constitution 
of  bodies,  and  is  therefore  distinguished  from  chemical  or 
any  other  species  of  action.* 

4.  In  Natural  Philosophy,  machines  are  spoken  of  as 
being  of  two  kinds — simple  and  complex.  A simple  ma- 

* In  scientific  works,  the  term  mechanics  is  usually  restricted  to  the 
action  of  solids,  while  mechanical  or  mechanically  is  applied  to  the  ac- 
tion of  both  solids  and  fluids.  For  example,  the  wearing  away  of  stone 
by  the  action  of  water,  is  said  to  be  mechanical  action,  or  that  the  wa- 
ter acts  mechanically . 


1.  Define  the  science  of  Mechanics,  and  the  word  itself. 

2.  How  is  mechanical  distinguished  from  chemical  force  ? 

3.  How  are  machines  divided  primarily  1 


9 


10 


MECHANICAL  POWERS. 


chine  is  equivalent  to  a tool  or  instrument,  and  a complex 
machine  is  an  engine,  in  which  different  parts  combine  to 
produce  the  required  effect.  In  common  phraseology, 
these  distinctions  are  not  very  minutely  attended  to. 

5.  Machines  are,  under  all  denominations  or  circum- 
stances, only  instruments  through  which  power  may  be 
made  to  act.  They  only  convey,  regulate,  or  distribute, 
the  force  or  power  which  is  communicated  to  them  from 
some  source  of  motion,  and  never  create  or  generate  power. 
But  although  a machine  does  not  create  power,  or  give 
more  power  than  it  has  received,  it  practically  applies  the 
power  which  has  been  communicated  to  it,  in  so  conve- 
nient and  easy  a manner,  that  a result  ensues  almost  as 
surprising  as  if  it  had  actually  generated  the  whole  or  a 
portion  of  the  power  it  exhibits. 

6.  The  main  purpose  required  in  mechanical  operations 
is  to  overcome,  oppose,  or  sustain,  a certain  resistance  or 
force.  'This  purpose  is  obtained  by  applying  another  species 
of  force.  According  to  the  usual  phraseology,  the  resist- 
ance or  force  to  be  overcome  is  called  the  weight,  and  the 
force  which  is  applied  is  called  the  power. 

7.  The  ability  of  applying  force  by  the  human  hands, 
without  the  aid  of  instruments  or  machines,  is  very  limited. 
In  almost  all  our  operations  of  art,  it  is  found  necessary  to 
call  in  the  aid  of  instruments  or  machines  of  some  kind. 
All  the  instruments  which  mankind  have  adopted  for  their 
use — from  a piece  of  stick  with  which  the  savage  scratches 
the  ground  as  a plough,  to  the  most  elegant  piece  of  mech- 
anism— act  upon  certain  fixed  principles  in  nature,  which 
a long  course  of  experience  and  scientific  investigation  has 
developed. 

8.  The  mechanical  powers,  which  exhibit  the  working  of 
these  principles,  are  strictly  only  three  in  number,  namely — 

1.  The  Lever. 

2.  The  Pulley,  or  Cord. 

3.  The  Inclined  Plane. 


4.  What  part  do  they  enact  ? 

5.  What  is  the  main  purpose  of  mechanical  operations  1 

6.  Define  the  weight  and  power  in  this  relation. 

7.  The  importance  and  variety  of  machinery. 


MECHANICAL  POWERS. 


11 


These  may  be  called  the  Primary  Mechanical  Powers  ; 
and  from  two  of  them,  the  Lever  and  Inclined  Plane,  other 
three  are  formed,  as  follow — 

1.  Wheel  and  Axle,  from  the  Lever. 

2.  Wedge,  from  the  Inclined  Plane. 

3.  Screw,  from  the  Inclined  Plane. 

These  may  be  called  the  Secondary  Mechanical  Powers. 
The  six  altogether  form  the  elements  of  every  species  of 
machinery,  however  complex. 

OF  LEVERS. 

9.  The  lever  is  one  of  the  most  important  and  exten- 
sively used  of  all  the  mechanical  powers,  and  its  operation 
exhibits  some  of  the  leading  principles  in  mechanics. 

10.  A lever  is  a rod,  or  bar  of  iron,  wood,  or  any  other 
material  which  is  moveable  upon  or  about  a prop  or  ful- 
crum, or  about  a fixed  axis.  It  is  called  a lever,  from  a 
French  word  signifying  to  raise,  and  has  been  applied  to 
instruments  for  raising  or  lifting  weights. 

11.  Three  elements  contribute  to  the  operation  of  the 
lever — the  power , the  fulcrum,  and  the  weight.  The  power 
is  the  force  applied,  the  fulcrum  is  the  prop  or  support,  and 
the  weight  is  the  resistance  or  burden  to  be  lifted.  The 
terms  power  and  weight  have  merely  a reference  to  the 
manner  in  which  the  machine  is  used  ; strictly,  both  the 
power  and  the  weight  are  forces  the  same  in  character  and 
action. 

12.  There  are  three  kinds  of  levers,  differing  according 
to  the  relative  situation  of  the  power,  fulcrum,  and  weight. 
Each  of  these  kinds  consists  of  a straight  bar,  and  in  theo- 
retical calculations  is  supposed  to  be  in  itself  destitute  of 
any  gravity  or  degree  of  heaviness.  In  theory,  also,  the 
forces  which  are  applied  are  supposed  to  act  at  right  angles 
to  the  fulcrum. 

S.  Name  the  primary  mechanical  powers,  and  the  secondary. 

9.  Whence  are  the  latter  derived  ? 

10.  Define  a lever. 

11.  What  elements  are  concerned  in  its  action  ? 

12.  Define  each  of  these  and  which  are  forces. 

13.  Varieties  of  levers,  and  theory  of  their  action. 


12 


FIRST  KIND  OF  LEVER. 


13.  In  the  first  or  most  simple  kind  of  lever,  “ the  ful- 
crum is  disposed  between  the  power  and  the  weight.”  In 
the  second  kind,  “ the  weight  is  disposed  between  the 
power  and  the  fulcrum.”  In  the  third  kind,  “ the  power  is 
disposed  between  the  weight  and  the  fulcrum.” 

FIRST  KIND  OF  LEVER. 

14.  In  the  first  kind  of  lever,  “ the  fulcrum  is  disposed 
between  the  power  and  the  weight.”  Figure  1,  is  an  ex- 

Figure  l.  ample.  A to  B is  a straight 

=gf  bar,  resting  on  a prop  or  ful- 
i crum  F.  From  A to  F is  the 
w«  long  arm  of  the  lever, and  from 
F to  B is  the  short  arm.  P is  the  power,  or  a certain  force 
drawing  down  the  extremity  of  the  long  arm  at  A.  W is 
the  weight  suspended  from  the  extremity  of  the  short  arm 
at  B.*  The  object  is,  to  cause  P,  which  is  supposed  to  be 
a small  weight,  to  balance  or  overcome  W,  which  is  sup- 
posed to  be  a weight  much  heavier.  Practically,  the  force 
of  a man  pressing  upon  the  extremity  of  the  handle  of  the 
lever  at  A,  will  effect  with  ease,  in  lifting  the  heavy  weight 
W,  what  it  would  require  a much  greater  force  to  accom- 
plish by  pressing  upon  the  long  arm  at  a point  half  way 
betwixt  A and  the  fulcrum.t 

15.  This  is  more  clearly  exemplified  in  figure  2,  which 

represents  a lever  placed 
conveniently  for  raising  a 
square  block  W,  which  is 
the  weight.  On  pressing 
down  the  extremity  of  the 
long  arm  of  the  lever  at 

* Some  authors  call  the  long  arm  the  arm  of  the  power,  and  the  short 
arm  the  arm  of  the  weight. 

t Note  1. — Properly  speaking,  the  power  does  not  sustain  the  weight, 
for  both  are  supported  by  the  fulcrum  ; the  power,  in  the  case  of  equi- 
librium, only  prevents  the  weight  from  producing  a motion  of  rotation. 

Note  2. — In  every  machine,  simple  or  complex,  besides  the  power 
required  to  balance  the  resistance,  there  must  be  some  additional 
power  applied  in  order  to  produce  motion,  or  overcome  the  inertia  of 
rest  of  the  body. 

14.  Define  each  of  the  three  in  the  arrangement  of  the  forces. 

15.  Explain  the  diagram,  and  the  notes. 


Figure  2 


FIRST  KIND  OF  LEVER. 


13 

A,  the  point  of  the  short  arm  B raises  the  block.  F is 
an  object  lying  on  the  ground  to  press  against  as  the  ful- 
crum. As  in  the  case  of  figure  1,  “ the  force  of  a man 
pressing  upon  the  extremity  of  the  handle  at  A,  will  effect 
with  ease,  in  lifting  the  weight  W,  what  it  would  require  a 
much  greater  force  to  accomplish  by  pressing  upon  the  long 
arm  at  a point  half  way  betwixt  A and  the  fulcrum.” 

1G.  The  principle  in  mechanics  which  produces  this 
phenomenon  is  very  simple,  and  is  explained  by  what  is 
called  the  Law  of  Virtual  Velocities,  or,  from  its  gene- 
ral application,  the  Golden  Rule  of  Mechanics. 

17.  This  law  or  rule  is,  that  a small  weight, descend- 
ing a LONG  WAY,  IN  ANY  GIVEN  LENGTH  OF  TIME,  IS  EQUAL 
IN  EFFECT  TO  A GREAT  WEIGHT  DESCENDING  A PROPORTION- 
ABLY  SHORTER  WAY  IN  THE  SAME  SPACE  OF  TIME.  In  Other 

words,  what  is  gained  in  velocity  or  time,  is  lost  in  expen- 
diture of  power. 

18.  Another  way  of  stating  this  important  law  is  as 
follows: — In  the  case  of  equilibrium,  if  a motion  be 

GIVEN  TO  THE  MECHANICAL  POWER,  THEN  THE  POWER  MUL- 
TIPLIED BY  THE  SPACE  THROUGH  WHICH  IT  MOVES,  IN  A 
VERTICAL  DIRECTION,  WILL  BE  EQUAL  TO  THE  WEIGHT  MUL- 
TIPLIED BY  THE  SPACE  THROUGH  WHICH  IT  MOVES  IN  A 
VERTICAL  DIRECTION. 

19.  This  principle,  which  applies  to  every  mechanical 
movement  in  the  case  of  equilibrium,  has  been  illustrated 
by  a reference  to  the  property  of  attraction  of  gravitation. 
What  is  called  weight,  is  only  an  effect  of  gravity  on  the 
atoms  of  matter.  In  figurative  language,  every  atom  is 
drawn  towards  the  earth  by  an  invisible  line  or  cord  of 
attraction ; and  when  one  atom  rises  or  falls  ten  inches,  the 
same  quantity  of  attraction  is  drawn  out  from,  or  sent 
back  to  the  earth,  as  if  ten  atoms  were  to  rise  or  fall  only 
one  inch. 

20.  Thus,  by  a proper  mode  of  applying  the  power,  we 


16.  What  of  this  diagram  ? 

17.  By  what  names  has  this  principle  of  action  been  called  J 

18.  What  is  this  law,  and  how  stated  1 

19.  What  of  atomic  gravitation  ? 

20.  What  illustration  is  stated  ? 


1 1 


FIRST  KIND  OF  LF.VKR. 


may  cause  a weight  of  one  pound,  by  moving  through  a 
space  of  ten  feet,  to  raise  another  weight  of  ten  pounds, 
moving  through  a space  of  one  foot;  or  (the  reverse)  by  a 
weight  of  ten  pounds  moving  through  the  space  of  one  foot, 
we  may  make  a single  pound  move  through  the  space  of 
ten  feet.  But  by  none  of  the  mechanical  powers  shall  we 
be  able,  by  moving  a weight  of  ten  pounds  through  one 
foot,  to  move  a single  pound  through  eleven  feet ; nor,  by 
a single  pound  moving  through  a space  of  nine  feet,  shall 
we  be  able  to  raise  a weight  of  ten  pounds  through  ode 
foot. 

21.  Neither  by  the  power  of  the  lever,  therefore,  nor  by 
any  other  of  the  mechanical  powers,  can  we  make  any  abso- 
lute increase  of  the  power  which  is  applied.  In  other 
words,  the  quantity  of  power  expended  in  any  great  and 
instantaneous  effort,  is  exactly  the  amount  of  the  power 
which  has  been  previously  accumulated.  All  that  w?e  can 
do  to  procure  mechanical  advantage,  is  to  accommodate 
the  velocity,  force,  or  direction  of  the  applied  power,  to  the 
purposes  which  we  may  have  in  view. 

22.  To  apply  this  principle  to  the  lever,  figure  1 or  2,  a 
small  force  at  A is  equal  to  double  the  force  exerted  at  a 
point  half  way  betwixt  A and  the  fulcrum,  yet,  in  both 
cases,  the  same  amount  of  mechanical  power  is  expended. 
A slight  push  downwards  at  A,  by  being  continued  for  one 
minute,  is  equal  te  a push  of  double  the  force  at  a point 
half  way  towards  the  fulcrum,  continued  for  the  same  time. 
Any  amount  of  force,  therefore,  can  be  exerted  urith  ease 
at  the  extremity  of  the  long  arm  of  the  lever,  provided  we 
choose  to  make  the  arm  long  enough  and  strong  enough. 

23.  It  may  possibly  be  said  that  it  would  be  as  expedi- 
tious to  push  down  the  extremity  of  the  long  arm  of  the 
lever,  as  to  push  dowm  the  arm  at  a point  nearer  the  ful- 
crum. Practically,  in  small  levers  this  may  be  the  case ; 
but  when  levers  of  considerable  length  have  to  be  used, 
and  a succession  of  depressions  and  raisings  are  necessary, 
it  will  be  found  that  more  time  is  spent  in  working  with  a 

21.  What  of  the  increase  of  power,  not  absolute  ? 

22.  How  is  this  explained  ? 

23.  What  of  long  and  short  levers  ? 


FIRST  KIND  OF  LEVF.R. 


15 


long  than  a short  lever.  For  when  the  sweep  of  the  lever 
is  inconveniently  long,  the  person  using  it  has  to  move  his 
body  quickly  up  and  down  over  a larger  space,  and  is  sooner 
fatigued.  For  this  reason,  although  a boy  with  a long  lever 
may  balance  as  great  a weight  as  a man  with  a shorter  one, 
yet,  in  raising  weights  successively  by  it,  the  boy  would  be 
sooner  fatigued. 

24.  It  is  a general  rule  that  “the  force  of  the  lever 
increases  in  proportion  as  the  distance  of  the  power  from 
the  fulcrum  increases,  and  diminishes  in  proportion  as  the 
distance  of  the  weight  from  the  fulcrum  diminishes.”  In 
making  calculations  to  ascertain  the  proportions  to  be  ob- 
served betwixt  the  power  and  the  weight,  regard  must  be 
paid  to  the  respective  lengths  of  the  long  and  short  arms 
of  the  lever.  We  must  also  tix  what  are  to  be  the  units  of 
weight  and  distance,  and  let  them  be  the  same  on  both 
ends.  If  we  state  inches  to  be  the  unit  of  length  of  the 
short  arm,  inches  must  be  the  unit  of  length  of  the  long 
arm;  and  in  the  same  manner,  if  ounces  be  made  the  unit 
of  weight  of  the  short  arm,  ounces  must  be  made  the  unit 
of  power  of  the  long  arm. 

25.  Rule. — Multiply  the  weight  by  its  distance  from  the 
fulcrum;  then  multiply  the  power  by  its  distance  from  the 
same  point,  and  if  the  products  are  equal,  the  weight  and 
the  power  will  balance  each  other. 

26.  Example  first. — Suppose  a weight  of  100  pounds 
on  the  short  arm  of  a lever,  at  the  distance  of  8 inches  from 
the  fulcrum,  then  another  weight  or  power  of  8 pounds 
would  be  equal  to  this,  at  the  distance  of  100  inches  from 
the  fulcrum.  Because  8 multiplied  by  100  produces  800, 
and  100  multiplied  by  8 produces  800— and  thus  the  weight 
and  the  power  would  mutually  counteract  each  other. 

27.  Example  second. — Suppose  we  wish  to  calculate 
what  power  should  be  employed  at  the  end  of  the  long 
arm  of  a lever  to  balance  a given  weight  at  the  end  of  the 
short  arm.  We  multiply  the  weight  by  the  length  of  i:s 


24.  What  general  rule  is  stated  1 

25.  How  are  the  proportions  to  be  calculated  ? 

26.  Give  the  rule,  with  examples. 


in 


FIRST  KIND  OF  T.F.VFR. 


nrm.  This  gives  us  a product  ; then  divide  that  product 
by  the  number  of  inches  in  the  long  arm,  and  the  result  or 
quotient  is  the  power.  Thus,  a weight  of  10  pounds  mul- 
tiplied by  10  inches,  as  the  length  of  the  short  arm,  gives 
a product  of  100.  If  the  length  of  the  long  arm  be  20, 
we  find  how  many  twenties  are  in  100,  and  there  being  5, 
consequently  5 pounds  is  the  power.  In  this  instance,  the 
mechanical  advantage  is  two  to  one — that  is,  the  power  is 
twice  as  small  as  the  weight. 

28.  The  common  spade  used  in  delving  in  gardens  offers 
a familiar  example  of  simple  lever  power,  when  employed  in 
raising  the  earth  from  its  place  to  turn  it  over.  Figure  3 
represents  an  equally  familiar  example,  namely,  a wood- 

Figure  3. 


sawyer  or  carpenter  moving  a log  of  timber  from  its  place, 
by  means  of  a long  pole  or  beam  of  wood.  Stone  masons 
use  a lever  of  iron  of  this  description,  called  a crow-bar. 

29.  The  ancient  Egyptians  were  acquainted  with  the 
power  of  the  lever,  and  employed  it  to  raise  the  large 
blocks  of  stone  of  which  the  Pyramids  are  composed.  The 
lever  used  by  them,  however,  was  of  a rude  description, 
and  required  many  men  to  wield  it.  According  to  Hero- 
dotus, a Greek  historian,  who  writes  of  Egypt,  it  consisted 
of  a beam  of  wood,  fixed  by  a joint  or  axle  on  an  upright 
frame,  which  was  the  fulcrum.  The  longer  arm  of  this 
lever  was  several  times  the  length  of  the  shorter  arm.  To 
lift  each  block,  it  was  necessary  to  employ  two  of  these 


27.  What  familiar  illustrations  are  cited  1 

28.  What  ancient  levers  are  described  1 


FIRST  KIND  OF  DEVER. 


17 


Figure  4. 


levers,  with  ropes  attached,  one  lever  at  each  end  of  the 
block.  A number  of  men  were  employed  to  pull  the  ropes, 
as  represented  in  figure  4.  After  the  block  was  raised 
one  step  up  on  the  exterior  of  the  pyramid,  the  levers  were 
lilted  up  another  step  higher,  and  the  block  raised  to  their 
level.  In  this  clumsy  and  tedious  manner  were  the  Pyra- 
mids of  Egypt  erected.*  In  modern  times,  the  principle 
of  the  lever  is  employed  in  a much  more  speedy  and  effica- 
cious manner  in  raising  or  lowering  blocks  of  stone  for 
masonry,  or  in  loading  and  unloading  bales  of  goods  in 
commerce,  by  means  of  a machine  called  a crane,  hereafter 
to  be  described. 

30.  The  power  of  the  first  kind  of  lever  is  frequently 

seen  to.  operate  in  machines 


Figure  5. 


or  instruments  having  two 
arms.  The  most  common 
examples  of  this  nature  are 
pincers,  scissors,  and  simi- 
lar instruments.  In  a pair 
of  scissors  here  represent- 
ed. the  two  limbs  are  seen 


* To  erect  one  pyramid  alone,  called  the  Great  Pyramid,  required 
the  work  of  100,000  men  for  twenty  years  ; and  although  these  men 
were  compelled  to  work  without  wages,  like  slaves,  the  expense 
incurred  was  enormous.  In  the  present  day,  the  steam-engines  of 
England,  by  a united  effort,  cor  lift  the  whole  of  the  stones  of  the 
Great  Pyramid  into  their  places  in  about  twenty  hours. 


29.  How  would  such  machines  be  regarded  now  f 

30.  By  what  means  would  the  moderns  do  such  work  I 

31.  Explain  the  second  diagram. 

32.  What  do  we  iear.  in  the  note  1 


13 


FIRST  KIND  OF  LEVER. 


to  be  joined  with  a rivet  at  the  centre,  which  is  the  ful- 
crum of  both. 

31.  A common  scale  beam  for  weighing,  used  by  shop- 
keepers, is  an  example  of 
the  first  kind  of  lever 
formed  with  two  arms  of 
equal  length,  and  suspend- 
ed over  the  centre  of  gra- 
vity, so  that  the  two  extre- 
mities balance  each  other. 
See  figure  G.  Sis  a string  or 
line  suspending  the  beam 
A B at  a central  point  F, 

which  is  the  fulcrum.  The  point  of  suspension  or  pivot  is 
sharpened  to  a thin  edge,  so  as  to  allow  the  arms  to  rise  or 
fall  with  as  little  friction  as  possible,  when  any  thing  is  put 
in  the  scales. 

32.  There  is  another  kind  of  balance,  called  a steelyard, 
which  consists  of  a lever  with  arms  of  unequal  length,  and 
acts  upon  the  principle  of  distance  from  the  fulcrum  on 
the  long  arm  compensating  for  weight  on  the  short  arm 
as  defined  in  paragraphs  26  and  27.  Figure  7 is  a repre- 
sentation of  the  steelyard  balance.  C is  the  fulcrum  or 
pivot  by  which  the  beam  is  suspended,  and  freely  plays  as 
on  an  axis.  A is  the  short  arm,  and  the  opposite  end  is 

Figure  7. 


Figure  6. 


33.  Explain  the  first  diagram,  and  its  action. 

34.  What  of  the  second  ? 


FIRST  KIND  OF  LEVER. 


19 


the  long  arm.  W is  the  scale  for  the  reception  of  the  article 
to  be  weighed.  The  long  arm  is  graduated  into  divisions 
by  marks,  each  mark  denoting  by  a figure  a certain  num- 
ber of  pounds  or  "Dunces,  P is  a weight  of  a certain  heavi- 
ness, and  being  moveable  by  a ring,  it  can  be  slipped  along 
the  bar  to  any  required  point.  The  same  weight  is  always 
used,  and  thus  constitutes  one  of  the  principal  conveniences 
of  this  kind  of  balance.  In  proportion  as  the  article  to  be 
weighed  in  the  scale  W is  heavy,  so  is  the  weight  P slip- 
ped along  to  a greater  distance  from  the  fulcrum  ; and  when 
it  is  brought  to  a point  where  it  balances  the  article,  the 
figure  on  the  bar  at  that  point  indicates  the  amount  of  the 
weight.  If  P be  one  pound,  and  if,  when  suspended  from 
the  division  at  (5,  it  balance  the  weight  at  W,  it  is  evident 
that  the  weight  will  be  six  times  P,  or  six  pounds  And 
so  on  with  all  the  other  divisions. 

33.  The  steelyard,  though  not  so  ancient  as  the  common 
balance,  is  of  considerable  antiquity.  It  was  used  by  the 
Romans,  and  has  long  been  in  use  among  the  Chinese. 
Neither  the  common  balance  nor  the  steelyard  is  suitable 
for  showing  the  varying  weight  or  heaviness  of  an  article 
at  different  latitudes  of  the  earth’s  surface,  because  the 
weights  employed  are  equally  affected  with  the  attraction 
of  gravitation  and  centrifugal  force,  as  the  article  to  be 
weighed.  For  this  reason  the  difference  of  weight  result- 
ing from  the  causes  mentioned,  can  only  be  demonstrated 
by  a balance  formed  of  a spring  of  elastic  metal.  By 
suspending  the  article  from  the  spring,  it  pulls  it  out  to 
a certain  extent,  and  so  indicates  the  weight  on  a gradu- 
ated scale  on  the  instrument.  As  the  spring  acts  the  same 
in  all  latitudes,  it  serves  as  a fixed  or  unalterable  power, 
while  the  article  to  be  weighed  is  liable  to  an  alteration  in 
its  weight  or  heaviness  according  as  it  is  brought  near  or 
carried  from  the  equator.* 

* See  explanation  of  variability  of  weight  in  paragraph  68,  Law, 
Matter,  and  Motion. 


35.  What  objection  lies  against  both  ? 

36.  What  of  the  spring  balance  ? 


20 


SECOND  KIND  OF  LEVER. 


SECOND  KIND  OF  LEVER. 


FA 


nw 


34.  In  the  lever  of  the  second  kind,  the  weight  is  placed 

Figure  8.  between  the  power  and  the  ful- 

2)  crum,  as  in  figure  8.  The  line 

from  A to  B is  the  long  aru; ; B 
to  F is  the  short  arm.  W is  the 
weight,  and  P is  the  power.  The 
object  required  by  this  lever  is  to 
lift  the  weight  W by  raising  the  extremity  of  the  lever  at  A. 
In  this  as  in  the  case  of  the  first  kind  of  lever,  the  power 
is  increased  in  proportion  to  its  distance  from  the  fulcrum. 

35.  Examples  of  this  kind  of  lever  power  are  common. 
One  of  the  most  familiar  is 
that  of  a man  pushing  or  lift- 
ing forward  a bale  of  goods, 
as  represented  in  figure  9,  in 
which  the  bale  or  weight  W 
presses  against  the  lever  be- 
tween the  power  P and  the 


Figure  9. 


fulcrum  F. 

36.  Another  example  of  the  second  kind  of  lever  is  that 
of  a man  using  a wheelbarrow, 
as  represented  in  figure  10.  A 
point  in  the  wheel  of  the  bar- 
row  where  it  presses  on  the 
ground,  is  the  fulcrum.  The 
body  of  the  barrow,  with  us 
load,  is  the  weight.  And  the 
two  handles  lifted  or  held  up 
by  the  man  form  the  power.  In 

proportion  as  the  man  shortens  or  lengthens  the  handles  in 
holding  them,  so  does  he  increase  or  diminish  the  weight 
he  has  to  sustain. 

37.  Two  men  carrying  a load  between  them  on  a pole 
is  also  an  example  of  the  second  kind  of  lever.  The  load 
may  either  rest  upon  or  be  dependent  from  the  pole.  In 


Figure  10. 


37.  Define  the  second  kind  of  lever. 

38.  What  of  each  of  the  diagrams  1 

39.  What  of  the  two  diagrams  ? 


SECOND  KIND  OF  LEVER.  21 

the  case  of  two  porters  carrying  a sedan  chair,  by  means  of 
two  poles,  the  load  or  weight  is  partly  above  and  partly  below 
the  line  of  the  lever.  In  the  case  of  porters  carrying  a barrel 

slung  from  a pole,  as  in  figure 
11,  the  weight  is  altogether  be- 
low the  lever.  In  both  instan- 
ces the  principle  is  the  same. 
Each  man  acts  as  the  power 
in  moving  the  weight,  and  at 
the  same  time  each  man  be- 
comes a fulcrum  in  respect  to 
the  other.  If  the  weight  hang 
fairly  from  the  centre  of  the  pole,  each  man  will  bear  just  a 
half  of  the  burden  ; but  if  the  weight  be  slipped  along  to  be 
nearer  one  end  of  the  lever  than  the  other,  then  the  man 
who  bears  the  shorter  end  of  the  pole,  supports  a greater 
load  than  the  man  who  is  at  the  long  end.  The  weight 
increases  precisely  in  proportion  as  it  advances  towards 
him.  Sometimes,  when  a man  and  a boy  are  carrying  a 
hand-barrow  between  them,  the  man,  in  order  to  ease  the 
weight  as  much  as  possible  to  the  boy,  holds  by  the  arms 
of  the  barrow  near  to  where  they  join  the  loaded  part. 

38.  In  yoking  horses  to  the  extremities  of  cross  bars  in 
ploughs,  coaches,  or  other  vehicles,  care  requires  to  be 
taken  to  hook  the  cross  bar  to  the  load  at  its  centre,  other- 
wise one  horse  will  have,  to  pull  more  than  the  other. 

39.  An  inflexible  beam  resting  on  supports  or  fulcra  at 
its  two  extremities,  acts  similarly  as  a lever  of  the  second 
kind.  Should  no  weight  be  appended  to  its  centre,  the 
weight  of  the  material  itself,  when  the  extension  is  consid- 
erable, will  be  enough  to  bend  it  down,  and  even  to  break 
it.  Extended  flexible  cords  or  chains,  are  from  this  cause 
always  bent  down  in  the  middle,  no  power  of  extension 
being  able  to  overcome  the  gravity  of  the  materials,  which 
will  give  way  before  they  can  be  rendered  perfectly  straight. 
The  bended  string  of  a boy’s  paper  kite  is  an  example  of 
this  powerful  influence  of  gravity  of  materials. 


40.  What  of  the  weight  of  the  material  itself  ? 

41.  What  of  the  string  of  a kite  ? 


22 


SECOND  KIND  OF  LEV  TK. 


40.  The  instrument  used  for  cracking  nuts  (figure  IT: 
is  an  example  of  the  second  kind  of  lever  with  two  arms  or 

Figure  12.  limbs.  The  fulcrum  is  the  joint  which 
connects  the  two  limbs;  the  nut  be- 
tween them  is  the  weight  or  resistance ; 
and  the  hand  which  presses  the  limbs 
together,  in  order  to  break  the  nut,  is  the  power.  As  each 
limb  is  a lever,  a double  lever  action  takes  place  in  the 
operation. 

41.  The  oar  of  a boat  in  rowing  is  a lever  of  the 
second  kind.  The  hands  of  the  sailor  who  pulls  constitute 
the  power;  the  boat  is  the  weight  to  be  moved ; and  the 
water  against  which  the  blade  of  the  oar  pushes,  is  the  ful- 
crum. 

42.  The  second  kind  of  lever  is  sometimes  employed  as 
an  instrument  of  pressure.  The  point  of  the  short  arm  is, 
for  example,  pushed  into  a crevice  or  hole  in  a wall,  the 
fulcrum  is  the  object  to  be  pressed,  and  at  the  extremity  of 
the  long  arm  a heavy  weight  is  applied.  In  this  rude  but 
efficacious  manner  are  cheeses  pressed  in  some  parts  of  the 
country. 


Figure  13. 


THIRD  KIND  OF  LEVER. 

43.  In  the  lever  of  the  third  kind,  the  power  is  placed 
between  the  weight  and  the  ful- 
crum. Figure  13.  The  fulcrum 
is  at  the  extremity  of  the  short  arm 
at  F ; the  weight  VV  is  dependent 
from  the  extremity  of  the  long  arm 
at  A ; and  P is  the  power. 

44.  In  this  kind  of  lever,  the  power  acts  with  consider  - 
ble  disadvantage,  or  with  small  effect;  but  this  disadvantage 
is  compensated  by  an  opposite  advantage,  which  is  frequently 
of  great  importance  in  the  operations  of  both  nature  and 
art.  The  advantage  consists  in  the  velocity  with  which  a 
small  power  will  cause  the  extreme  point  of  the  long  arm 


42.  Explain  the  first  diagram. 

43.  What  of  rowing  a boat,  and  of  pressing  cheeses  t 

44.  Explain  the  second  diagram. 


THIRD  KIND  OF  LEVER. 


Figure  14. 


of  the  lever  to  move  over  a great  space.  This  lever,  theio- 
fore,  whether  in  nature  or  art,  is  used  only  when  a great 
space  has  to  be  traversed  quickly  by  the  long  arm  ; but  in 
tins  case,  the  power  must  always  be  greater  than  the  weight. 

45.  An  example  of  this  kind  of  lever  is  found  in  the 
foot-board  of  the  turning-lathe. 
Figure  14.  The  foot  of  the  work- 
man presses  lightly  on  the  board 
or  plank  near  the  end  which  rests 
on  the  ground,  or  fulcrum,  and 
causes  the  opposite  extremity  of 
the  board  to  move  in  a downward 
direction  over  a considerable  space. 
A spring  over-head,  or  a crank, 
pulls  the  board  up  again  by  means 

of  a string  S;  the  workman  again  presses  it  downward,  and 
so  a constant  action  of  the  string  or  cord  which  works  the 
lathe,  is  easily  produced. 

46.  A man  wielding  a flail  with  two  hands,  and  similar 
instances  of  using  weapons,  are  also  examples  of  the  third 
kind  of  lever  action.  A similar  action  is  observable  when 
we  use  fire-tongs  ; a small  motion  of  the  fingers  near  the 
joint  of  the  instrument,  causes  the  legs,  which  are  two 
levers,  to  open  or  shut  over  a considerable  space. 

47.  Before  the  peculiar  advantages  of  this  kind  of  lever 
became  known,  or  were  appreciated,  it  was  called  the  losing 
lever. 

48.  The  movements  in  the  limbs  of  animals  are  gene- 
rally produced  by  the  action  of  this  kind  of  lever  power. 


45.  What  is  gained  by  this  kind  of  lever  1 

46.  Explain  the  first  diagram. 

47.  What  erroneous  name  was  formerly  given,  and  why  ? 

48.  What  example  is  found  in  animal  structure  1 


24 


COMPOUND  LEVERS. 


OF  COMPOUND  AND  BENT  LEVERS. 


COMPOUND  LEVERS. 


49.  When  several  levers  of  the  simple  kinds  are  con- 
nected together,  and  are  made  to  operate  one  upon  the 
other,  the  machine  so  formed  is  called  a Compound  Lever. 
In  this  machine,  as  each  lever  acts  with  a power  equal  to 
the  pressure  on  it  of  the  next  lever  between  it  and  the 
power,  the  force  is  increased  or  diminished  according  to 
the  number  or  kind  of  levers  employed. 

50.  Figure  15  represents  a compound  lever,  consisting 


of  three  simple  levers  of  the  first  kind,  placed  in  a line,  and 
each  working  on  its  own  fulcrum.  The  desired  object  of 
the  machine  is  for  a small  force  or  power  at  P,  to  move  or 
balance  a large  weight  at  W.  The  same  rule  applies,  in 
calculating  the  action  of  this  combined  lever,  which  has 
already  been  given  for  the  simple  lever,  namely,  “ multiply 
the  weight  on  any  lever  by  its  distance  from  the  fulcrum; 
then  multiply  the  power  by  its  distance  frocn  the  same 
point,  and  if  the  products  are  equal,  the  weight  and  the 
power  will  balance  each  other.”  Or,  for  the  form  of  lever 
in  the  figure,  “ multiply  the  length  of  the  long  arm  by  the 
moving  power,  and  multiply  that  of  the  short  one  by  the 
weight,  or  resistance.” 

51.  It  is  supposed  that  the  three  levers  in  the  figure  are 
of  the  same  length,  the  long  arms  being  six  inches  each, 


4i).  Define  a compound  lever. 

50.  Explain  the  second  diagram. 

51.  By  what  rule  is  the  force  of  this  combined  lever  calculated  t 


Figure  15. 


E 


COMPOUND  I.F.VFRS. 


2-r, 


mid  the  short  ones  two  inches  each  ; required — the  weight 
which  a moving  power  of  l pound  at  P will  balance  at  YV. 
In  the  first  place,  I pound  at  P would  balance  3 pounds  at 
E ; we  say  3,  because  the  long  arm  being  6 inches,  and 
the  power  I pound,  6 multiplied  by  1 is  ti ; and  the  short 
one  being  2 inches,  we  find  that  there  are  3 twos  in  6, 
therefore  3 is  the  weight.  The  long  arm  of  the  second 
lever  being  also  6 inches,  and  moved  with  a power  of  3 
pounds,  multiply  the  3 by  6,  which  gives  18 ; and  multiply 
the  short  arm,  being  2 inches,  by  a number  which  will  give 
18  ; we  find  that  9 will  do  so  (9  twos  are  18) ; therefore  9 
is  the  weight  borne  at  the  extremity  of  the  short  arm  of 
the  second  lever  at  D.  The  long  arm  of  the  third  lever 
being  also  6 inches,  and  moved  with  a power  of  9 pounds, 
multiply  the  9 by  6,  and  we  have  54;  and  multiply  the  short 
arm,  being  2 inches,  by  a number  which  will  give  54  ; we 
find  that  27  will  do  so  (twice  27  is  54) ; therefore  27  is  the 
weight  borne  at  the  extremity  of  the  short  arm  of  the  third 
lever.  Thus  I pound  at  P will  balance  27  pounds  at  YV. 
Or  1 ounce  at  P will  balance  27  ounces  at  YV — the  pro- 
portions being  always  alike,  whatever  denomination  of 
weight  we  employ. 

52.  In  this  instance,  the  increase  of  power  is  compara- 
tively, small,  because  the  proportion  between  the  long  and 
the  short  arms  is  only  as  2 to  6,  or  1 to  3.  If  we  make 
the  proportions  more  dissimilar,  as  1 to  10,  or  1 to  20,  the 
increase  of  force  becomes  very  great.  For  example,  let 
the  long  arms  be  18  inches  each,  and  the  short  ones  1 
inch  each,  and  1 pound  at  P will  balance  18  pounds  at  A, 
and  the  second  lever  will  be  pushed  up  with  a power  of  18 
pounds.  This  18  being  multiplied  by  the  length  of  the 
lever  18,  gives  324  pounds  as  the  power  which  would 
press  down  the  third  lever.  Lastly,  multiply  this  324  by 
the  length  of  the  lever  18,  and  the  product  is  5832  pounds, 
which  would  be  the  final  weight  at  YV  which  1 pound  at  P 
would  raise. 

53.  The  following  is  a general  rule  for  calculating  the 


52.  Repeat  the  calculations  of  these  three  levers. 

53.  How  may  the  force  be  increased  < 


26 


BENT  LEVERS. 


advantages  of  a compound  lever  consisting  of  anv  number 
of  levers,  whether  equal  or  not : — Cali  ihe  arms  of  the  de- 
ferent levers  next  the  power  the  arms  of  power , and  the 
other  arms  the  arms  of  weight;  then,  if  the  lengths  of  the 
arms  of  power  and  the  power  itself  be  successively  multi- 
plied together,  the  product  will  be  equal  to  the  continued 
product  of  the  arms  of  weight  and  the  weight,  when  the 
power  and  weight  are  in  equilibrium. 

54.  A similar  result  to  that  of  a combination  of  levers, 
might  be  produced  by  only  one  lever,  provided  it  were  long 
enough,  but  the  operation  would  be  both  clumsy  and  incon- 
venient. By  combining  levers,  and  making  them  act  one 
upon  another,  great  weights  maybe  balanced  within  a small 
compass,  and  with  an  exceedingly  small  power.  On  this 
account,  machines  are  constructed  with  combinations  of 
levers,  for  weighing  loaded  carts  and  other  heavy  burdens. 
The  cart  is  wheeled  upon  a sort  of  table  placed  level  with 
the  ground,  beneath  which  the  levers  are  arranged;  and  a 
small  weight  placed  on  a scale  attached  to  the  extreme 
point  of  the  first  lever,  balances  the  load,  which  rests  on 
the  table  above  the  last  lever.  This  species  of  weighing 
machine  is  often  to  be  seen  at  toll-bars. 

BENT  LEVERS.  * 

55.  In  the  foregoing  examples  of  lever  powers,  the  levers 
or  bars  are  supposed  to  be  straight,  and  the  powers  and 
weights,  or  forces,  are  supposed  to  act  at  right  angles  with 
them. 

56.  Levers  are  frequently  bent  in  their  form,  for  purposes 
of  convenience,  and  the  powers  and  weights  often  act 
obliquely , or  not  at  right  angles. 

57.  In  calculating  the  mechanical  advantage  of  bent 
levers,  the  chief  matter  for  consideration  is  obliquity  in  the 
direction  of  the  applied  power  and  weight.  Obliquity  in 
the  action  of  the  forces,  generally  diminishes  the  mechanical 
advantage. 

54.  What  of  the  arms  of  power  and  of  weight  1 

55.  To  what  uses  are  compound  levers  applied  ? 

56.  What  of  bent  levers  and  their  action  f 


LEVERS  <-»!■'  OBLKiUE  ACTION. 


27 


58.  Whatever  be  the  form  of  the  lever,  or  the  direction 
of  the  power  and  the  weight,  the  mechanical  advantage  of 
the  power  or  the  weight  is  always  represented  by  a line 
drawn  from  the.  fulcrum,  at  right  angles  to  the  direction  in 
which  the  forces  are  respectively  exerted. 


Figure  16. 


59.  Figure  16  is  a bent 
^lever,  with  the  power  P hang- 
ing from  A,  and  the  weight 
,W  hanging  from  B.  In  this 
case,  both  the  power  and  the 
weight  act  at  right  angles  to 
an  ideal  line, drawn  as  from  E 
to  G across  the  fulcrum,  which 
strikes  the  lines  of  direction 
of  the  forces  at  right  angles.  This  ideal  line,  therefore, 
represents  the  true  lever  of  calculation,  and  we  proceed  with 
it  according  to  the  ordinary  rule  for  calculating  lever  powers 
In  this  manner,  the  bending  goes  for  nothing. 


Figure  17. 


69.  Figure  17  is  a straight 
lever  with  the  power  P acting 
G obliquely  from  D to  A,  and  the 
* vveight  W acting  obliquely  from 
G to  B.  In  order  to  calculate 
the  power  of  this  kind  of  lever, 
we  must  draw  lines  as  represented  in  figure  18.  First,  we 
draw  a line  obliquely  upwards  in  the  direction  of  the  pulling 


Figure  18. 

M N 


power.  This  line  is  seen  dot- 
ted from  A to  M.  We  then 
draw  a line  off  from  it,  or  at 
right  angles  with  it,  to  F the 
ulcrum.  This  line  is  seen 
dotted  and  marked  H.  We 
next  draw  a line  obliquely  up- 
wards in  the  direction  of  the 
pull  of  the  weight,  as  from  B to  N ; and  in  the  same  manner 
as  bef  ire,  draw  a line  at  right  angles  from  it.  This  line 


57.  Explain  the  diagram. 

58.  Explain  the  first  diagram. 

59.  What  does  the  second  show  7 

60.  How  does  the  third  differ? 


28 


LEVERS  OF  OBLIQUE  ACTION. 


is  seen  doited  and  marked  K.  We  have  now  found  an 
ideal  lever,  with  two  arms,  H and  K.  This  jdeal  lever  is 
the  true  lever  of  calculation,  and  we  proceed  with  it  accord- 
ing to  the  ordinary  rule  for  calculating  lever  powers  (25). 
til.  The  next  example,  figure  19,  represents  the  power 


Figure  19. 


and  weight  acting  obliquely  the  same 
as  in  figure  18;  but  in  this  case  the 
lever  is  bent.  The  bending  of  the 
lever,  however,  does  not  affect  tiie 
rule  of  calculation,  which  is  the  same 
as  in  figure  18.  W e begin  by  draw- 
ing a line  obliquely  upwards  in  the 
direction  of  the  pulling  power.  This 
line  is  seen  dotted  from  A to  C.  We 
then  draw  a line  off,  from  it,  or  at  right  angles  with  it,  to  F 
the  fulcrum.  This  line  is  seen  dotted  from  C to  F.  We 
next  draw  a line  obliquely  upwards,  in  the  direction  of  the 
pull  of  the  weight;  and  in  the  same  manner  as  before, 
draw  a line  at  right  angles  from  it  (as  from  L),  to  F.  W e 
have  now  found  an  ideal  lever;  from  C to  F being  the  long 
arm,  and  F to  D the  short  arm.  This  ideal  lever  is  the 
lever  of  calculation,  and  we  proceed  with  it  according  to 
the  ordinary  rule  for  calculating  lever  powers  (25). 

Figure  20.  62.  Sometimes  the  lever  is  bent  in  such  a 

manner  that  the  long  arm  rises  perpendicularly 
from  the  fulcrum,  as  in  figure  20.  In  this 
case,  the  upright  long  arm  from  F to  A acts 
precisely  as  if  it  were  horizontal,  because  the 
power  or  hand  is  supposed  to  act  at  right 
B angles  to  the  arm.  If  we  were  to  draw  an 
ideal  line  from  the  t p of  the  arm  at  A directly 
in  downwards  to  F,  it  would  descend  straight 
: through  the  arm,  and  hence,  in  this  case,  there 
would  be  no  use  in  drawing  it.  The  calculation  may  be 
made  with  the  arm  itself. 


W< 


61.  What  of  ideal  levers,  and  their  uses  ? 

62.  Explain  each  of  the  diagrams. 


LEVERS  OF  OBLIQUE  ACTION. 


29 


Figure  21. 


63  But  if  the  power  be  made 
to  draw  obliquely  downward, or  not 
at  right  angles  to  the  line  from 
the  fulcrum,  we  must  draw' an  ideal 
line,  as  represented  in  figure  21. 
The  line  of  direction  of  the  power 
is  seen  proceeding  obliquely  from 
.A  to  the  hand  P.  A dotted  line 
H is  drawn  at  right  angles  from 
this  line  to  F the  fulcrum  ; the  line 
H therefore  represents  the  true  arm 


of  power  of  the  lever. 

64.  Suppose  the  line  of  direction  of  the  power  in  the 
last  figure,  had  been  drawn  slantingly  upward  instead  of 
dowmvard,  then  an  ideal  dotted  line  would  have  been  to  be 
drawn  obliquely  downward  from  it,  crossing  the  arm  at  A, 
and  a line  drawn  at  right  angles  from  it  to  F,  would  have 
represented  the  arm  of  power. 

Figure  22.  65.  The  adjoining  figure,  represent- 

ing a pronged  hammer  in  the  act  of 
being  employed  to  extract  a nail,  is  an 
example  of  a bent  lever,  resembling 
those  just  mentioned.  The  hand  of 
the  workman  is  the  pow'er  exerted  on 
the  long  arm  of  the  lever ; the  head  of 
the  hammer,  where  it  presses  on  the 
flat  surface  beneath  it,  is  the  fulcrum  ; 
the  prongs  are  the  short  arm  of  the 
lever,  and  the  resistance  of  the  nail  is  the  weight. 

66.  From  the  examples  now  given,  it  will  be  observed 
that,  whatever  be  the  shape  or  bending  of  the  lever,  and 
whatever  the  degree  of  obliquity  of  the  applied  force,  the 
pow'er  of  the  machine  may  be  calculated  by  drawing  ideal 
lines  at  right  angles  from  the  lines  of  the  forces  to  the 
fulcrum,  and  making  the  calculations  from  them. 


63.  How  are  calculations  made  in  all  cases  ? 


33 


LEVER  POWERS  RECAPITULATED. 


RECAPITULATION  OP  LEVER  POWERS,  AND 
ANIMAL  LEVERS. 

67.  To  avoid  confusion  or  misapprehension,  representa- 
tions of  the  three  kinds  of  levers  already  defined  are  here 
again  exhibited,  along  with  a few  brief  explanatory  obser- 
vations on  their  character  and  comparative  value.  For  the 
sake  of  clearness,  a hand  pulling  is  substituted  as  the  power. 
The  arm  of  the  power  is  used  to  signify  the  long  arm,  and 
the  arm  of  the  weight  the  short  arm. 

68.  Each  of  the  three  kinds  of  levers  has  its  own  special 
advantages,  and  is  peculiarly  adapt- 
ed to  certain  situations  and  pur- 
poses. In  a lever  of  the  first  kind, 
where  the  point  of  support  is  be- 
tween the  power  and  the  weight, 
either  the  power  or  the  weight  may 
have  the  advantage.  The  advan- 
tage varying  thus  between  the 

power  and  the  weight,  the  lever  of  the  first  kind  is  held  to 
be  most  convenient  tor  an  equilibrium  ; of  which,  as  has 
been  shown,  the  common  balance  affords  an  example. 

69.  In  the  lever  of  the  second  kind,  the  arm  of  the  power 


B figure  23. 


A 


»w 


Figure  24. 


B 


is  necessarily  longer  than  that  of  the 
weight  or  resistance,  since  the  resist- 
ance is  between  the  power  and  the  ful- 
crum, whilst  the  power  is  at  one  ex- 
tremily.  The  advantage  being  thus 
SVuhvays  in  favour  of  the  power,  the 
lever  of  the  second  description  is  al- 
ways favourable  for  overcoming  re- 
sistance. 

70.  In  the  lever  of  the  third  kind,  on  the  contrary,  the 
advantage  is  m favour  of  the  weight  or  resistance,  which 
is  placed  at  an  extremity,  while  the  power  lies  between  it 
and  the  point  of  support.  But  the  disadvantageous  position 


64.  What  kind  of  lever  is  shown  in  each  diagram  ? 

65.  Name  the  advantages  and  uses  of  each  kind. 


LEVER  IN  THE  HUMAN  ARM. 


31 


Figure  25. 


of  the  power  in  this  kind  of  lever  is  compensated  by  the 
extent  of  motion  which  necessarily  ensues  from  that  very 
disadvantage ; for,  the  closer  the 
power  is  to  the  fulcrum,  and  the 
farther  it  is  from  the  weight,  the 
more  extensive  and  rapid  is  the  mo- 
^ tion  to  which  the  weight  can  be 

subjected  on  the  slightest  action  of 

the  power.  The  lever  of  the  third 
kind,  therefore,  is  obviously  favour- 
l able  to  extensive  and  rapid  move- 

ments. 


ANIMAL  LEVERS. 


71.  A short  consideration  of  the  characteristic  advan- 
tages and  defects  attendant  on  each  of  the  three  kinds  of 
levers,  will  suffice  to  convince  us  of  the  superior  applica- 
bility of  the  third  kind  of  lever  to  the  purposes  of  animal 
motion.  Celerity  and  extent  of  motion,  it  is  obvious,  are 
here  objects  of  paramount  importance;  and  by  the  employ- 
ment chiefly  of  this  species  of  lever,  both  in  the  trunk  and 
the  limbs,  they  are  beautifully  and  effectually  attained.  In 
the  animal  machine,  the  bones  form  the  bases  or  arms  of 
the  levers  : the  muscle,  contractible  at  the  command  of  the 
will  or  fancy,  represent  the  potcer  ; the  joints,  th efulcrums 
or  points  of  support;  and  the  weight  of  the  body  or  of  in- 
dividual limbs,  as  it  may  happen,  constitutes  the  weight  or 
resistance,  increased,  as  in  the  case  of  the  hands  at  times, 
by  some  substance  carried  or  held  by  them.  The  most 
important  result  of  the  lever  powers  of  the  animal  machine, 
is  locomotion,  or  the  transmission  of  the  whole  body  from 
place  to  place.  [In  human  structure,  as  indeed  in  all  ani- 
mal organization.it  is  wonderful  to  observe  the  mechanism 
o the  Creator’s  wisdom  and  goodness,  anticipating  all  the 
boasted  discoveries  of  science,  and  plainly  teaching  the 
highest  lesson  in  practical  and  experimental  philosophy.] 

72.  The  spinal  or  vertebral  column,  when  we  regard  its 


6n.  What  of  the  bones,  muscles,  and  joints  of  animals  1 


32 


ANIMAL  LEVERS. 


motions  as  a whole,  represents  a lever  of  the  third  kind,  of 
which  the  fulcrum  is  in  the  articulation  of  the  last  bone  of 
the  column  with  the  sacrum  (the  bone  on  which  the  trunk 
rests) ; the  power  being  in  the  muscles,  which  are  inserted 
into  the  vertebral  column  along  its  course,  and  the  resist- 
ance in  the  weight  of  the  head,  neck,  and  trunk. 

73.  But  a much  more  dis- 


Figure  26. 


B 


Cw 


'F 

bow  to  the  wrist, 
w . Figure  28 


tinct  and  intelligib'e  example 
of  a lever  of  the  third  kind 
in  the  animal  frame,  is  exhib- 
ited in  the  human  arm.  A 
strong  muscle,  arising  in  the 
shoulder,  passes  down  in  front 
over  the  joint  of  the  elbow, 
and  is  inserted  into  one  of 
the  two  parallel  bones  which 
compose  the  frame  work  of 
1 the  lore-arm,  oi  from  the  el- 
On  being  contracted  in  the  slightest 
degree,  at  the  impulse  of  the  will,  this 
muscle  (the  power)  elevates  instantane- 
ously the  hand  (the  weight  or  resistance) 
to  the  shoulder,  bending  the  arm  upon 
the  elbow-joint,  (th e fulcrum).  Figure 
26  illustrates  perfectly  this  mechanism 
of  the  arm.  F represents  the  elbow- 
joint,  P the  power  or  will  acting  over, 
or  from  ihe  shoulder  S,  through  the 
contracting  muscle  M,  and  B the  arm 
from  the  hand  to  the  elbow,  while  the 
weight  W,  is  an  object  supposed  to  be 
laced  in  the  hand. 

74.  Nothing  can  better  illustrate  the 
characteristic  advantages  of  levers  of  the 
third  kind,  than  this  action  in  the  hu- 
man arm.  The  contraction  of  the  muscle 
to  the  extension  of  only  one  inch,  raises 


67.  What  of  the  spinal  column  ? 

68  Explain  the  diagram  mechanically. 
69.  What  does  this  diagram  show  1 


ANIMAL  LEVERS. 


33 


the  hand,  even  with  a very  considerable  weight  in  it,  through 
a semicircle  of  twenty-one  inches  ; and  by  relaxing  the  mus- 
cle only  a little,  the  hand,  as  represented  in  figure  27,  is 
allowed  to  drop  over  a similarly  wide  range.  No  doubt, 
other  muscles  in  the  arm  assist  in  this  action,  but  the  prin- 
cipal part  is  performed  by  the  one  described,  and  here  in- 
dicated by  the  letter  M. 

75.  It  is  worthy  of  observation,  that  in  the  second  of 
these  figures,  illustrating  the  mechanism  of  the  arm,  the 
lever  power  acts  under  increased  disadvantage  from  the 
greater  inclination  of  the  limb  than  in  the  preceding 
figure.  We  can  raise  or  sustain  a much  larger  weight 
with  the  hand  when  the  arm  is  bent  at  right  angles,  than 
when  it  is  extended  nearly  in  a straight  line;  and  the 
more  the  arm  is  stretched  out,  the  more  is  the  power  di- 
minished. What  is  gained,  however,  in  force,  is  neces- 
sarily lost  in  extent  of  motion. 

76.  A fine  example  in  the  animal  frame  of  the  lever  of 
the  third  kind,  where  extent  of  motion  was  not  the  object 
wanted,  as  it  is  in  the  arm,  is  seen  in  the  mechanism  of 
the  lower  jaw.  To  overcome  resistance,  was  in  this  case 
the  chief  end  required;  and,  acc  >rdingly,  we  find  a strong 
muscle  constituting  the  power,  passing  perpendicularly 
downwards  from  the  side  of  the  head  to  the  lower  jaw-bone, 
and  acting  on  it  in  a straight  line,  the  fulcrum  being  in  the 
articulation  of  the  jaw  near  the  ear.  The  force  with  which 
the  power  acts  in  this  case  is  immense,  particularly  when 
the  resistance  to  be  overcome  is  placed  near  the  fulcrum, 
or  directly  beneath  the  action  of  the  muscle.  We  take 
advantage  of  this  circumstance  in  cracking  nuts,  by  putting 
them  to  a certain  distance  back  between  the  jaws. 

77.  As  in  the  arms,  so  also  in  the  inferior  extremities, 
the  principal  muscles  hold  such  a relative  position  to  the 
bones  and  joints,  as  to  sustain  the  weight  of  the  b dy,  and 
transfer  it  al  ng  the  surface  of  the  ground,  with  all  the  ad- 
vantage of  a lever  power  of  the  third  kind.  If  the  mecha- 
nical action  of  the  muscles  and  bones  in  animals,  whether 
in  the  spinal  column  or  in  the  limbs,  had  been  arranged 


70.  What  of  the  muscle  of  the  jaw  ? 


•34 


ANIMAL  LEVERS. 


on  the  principle  of  either  of  the  other  descriptions  of  levers, 
the  requisite  contraction  in  the  length  of  the  acting  muscles 
would  have  been  so  great  as  to  render  the  shape  of  the 
limbs,  and  the- whole  figure  indeed,  extremely  clumsy,  and 
the  movements  very  inconvenient;  and  hence  the  wisdom 
of  the  existing  arrangement,  in  regard  to  simplicity,  beauty 
and  efficiency. 

78.  Examples  of  the  first  and  second  kinds  of  levers  are 
not  absent  in  the  animal  machine ; and  where  such  exam- 
ples occur,  they  uniformly  corroborate  what  has  been  said 
respecting  the  peculiar  character  of  each  of  the  three  kinds 
of  levers.  The  head,  for  instance,  requires,  for  the  fulfil- 
ment of  its  exalted  uses,  and  for  the  comfort  of  the  being, 
to  be  maintained  erect,  and  in  equilibrium.  A lever  of 
the  first  kind,  we  have  seen,  is  the  one  best  calculated  to 
effect  this  object,  and  accordingly,  such  a mechanism  is 
found  to  exist  here.  The  point  of  support  of  this  lever  is 
in  the  articulation  of  the  lateral  masses  of  the  two  first 
bones  of  the  spinal  column,  whilst  the  power,  and  the  re- 
sistance or  weight,  occupy  each  an  extremity  of  the  fever, 
represented,  the  one  by  the  face,  and  the  other  by  the  back 
part  of  the  head.  To  understand  this  fully,  it  must  be  ex- 
plained, that  the  point  of  support,  or  fulcrum,  on  which  the 
head  rests,  is  much  nearer  to  the  back  part  of  the  skull  ihan 
to  the  fore  part  or  face ; therefore,  this  forepart  (the  weight 
of  the  lever)  has  a tendency  to  fall  forwards,  but  is  retained 
in  equilibrium  by  the  strong  muscles  passing  from  the  lower 
parts  of  the  neck  to  the  hind  part  of  the  head  (which  is 
thus  rendered  the  site  of  the  power  of  the  lever.)  A perfect 
lever  of  the  first  kind  is  thus  made  the  agent  in  maintain- 
ing the  head  in  equilibrium 

79.  In  like  manner.it  might  be  shown,  that,  where  there 
is  a considerable  resistance  to  be  overcome,  the  bones  and 
muscles  are  so  arranged  as  to  represent  a lever  of  the  kind 
best  calculated  for  the  fulfilment  of  such  a purpose — namely, 
a lever  of  the  second  kind,  as  the  first  is  employed  when 
an  equilibrium  is  to  be  maintained,  and  the  second  when 
rapid  and  extensive  motion  is  to  be  produced. 


71.  Would  either  of  the  other  kinds  oflevers  have  been  as  well  l 

72.  Wli.it  example  of  the  first  kind  of  lever  is  cited  ? 


WHEELS. 


35 


OF  THE  WHEEL  AND  AXLE. 


80.  A lever  has  been  defined,  (10)  to  be  “ a rod  or  bar  of 
iron,  wood,  or  any  other  material  which  is  moveable  upon 
or  about  a prop  or  fulcrum,  or  about  a fixed  axis.” 

81.  The  illustrations  which  have  been  given,  show  the 
lever  only  in  its  character  of  a simple  bar,  which  is  move- 
able  in  some  part  “ upon  or  about  a prop  or  fulcrum.”  It 
is  now  to  be  shown  how  it  acts  when  moveable  upon  or 
about  a fixed  axis. 

82.  When  a lever  is  moveable  upon  an  axis,  and  is  sus- 
ceptible of  being  turned  completely  round,  it  assumes  the 
character  of  the  diameter  of  a wheel. 

83.  In  figure  28,  the  simple  rudiments  of  a wheel  are 
Figure  23.  represented.  A and  B are  the  two 

A F arms  of  a bar  or  lever  playing  upon  a 

fixed  axis  at  F,  and  which  axis  is  the 
fulcrum.  If  we  push  down  A,  we  raise  B,  or  if  we  push 
d >wn  B,  we  raise  A.  In  this  manner  the  situation  of  the 
power  and  the  weight  is  transferable  from  one  end  to  the 
other,  as  in  the  beam  of  a common  balance,  without  alter- 
ing the  equilibrium. 

Figure  29.  84.  Figure  29  is  a representation 

c of  awheel  in  a state  more  advanced 

to  completion.  Here  the  arms  AB 
are  connected  with  the  arms  DC, 
both  at  the  centre  F,  and  by  means 
B of  the  circumference  or  rim  of  the 
wheel.  By  reason  of  this  union  of 
parts,  the  central  axis  at  F becomes 
the  common  fulcrum  for  every  por- 
tion of  the  wheel ; therefore,  from 
the  centre  to  any  point  of  the  circumference  is  an  arm  of  a 
iever,  although  the  line  of  that  lever  be  not  marked  or  seen, 
as  in  the  case  of  a distinct  spoke. 

85.  A line  through  the  centre  from  one  side  of  the  cir- 


73.  What  of  the  wheel  and  axis  1 

74.  Explain  the  diagrams. 


36 


WHEEL  AND  AXLE PERPETUAL  LEVERS. 


cumference  of  a wheel  to  the  opposite  side,  is  the  diameter; 
from  the  centre  to  any  part  of  the  circumference,  is  the 
semi-diameter  or  radius.  The  arms  or  spokes  are  said 
to  radiate  from  a centre.  The  circumference  is  sometimes 
called  the  periphery. 

86.  Besides  wheels  with  axes  in  the  centre,  there  are 
wheels  with  axes  not  in  the  centre,  called  eccentric  wheels. 
At  present,  however,  we  are  treating  only  of  wheels  having 
i heir  axes  in  the  centre. 

87.  Wheels  with  a central  axis  may  be  rendered  avail- 
able as  levers  in  various  ways,  according  to  the  placing  of 
the  weight  or  resistance.  The  plan  commonly  pursued 
consists  in  giving  to  the  wheel  an  axle,  which  is  fixed  to  its 
arms,  and  placing  a weight  near  the  axle  or  fulcrum,  to 
work  against  another  weight  at  the  circumference. 

88.  Thus,  a machine  is  formed  called  the  Wheel  and 
Axle,  which  constitutes  one  of  the  simple  mechanical 
powers,  founded  on  the  lever. 

WHEEL  AND  AXLE. 

69.  The  machine  termed  the  Wheel  and  Axle  consists 
of  a wheel  fixed  upon  an  axle  or  spindle,  which  axle  turns 
horizontally  on  its  two  ends  in  upright  supports.  See  figure 
30.  The  fulcrum  of  the  ma- 
chine is  common  to  both  the 
wheel  and  the  axle,  and  is  the 
centre  of  the  axle.  A is  the 
wheel,  B is  the  axle,  and  H is  a 
handle  with  which  the  machine 
may  be  turned.  By  turning  the 
wheel,  the  axle  is  also  turned, 
and  a rope  being  fixed  to  the 
axle,  with  the  weight  W hang- 
ing at  its  extremity,  the  turning 
of  the  wheel  causes  the  axle  to  wind  up  the  rope,  and  so 
’lift  the  weight.  If,  instead  of  turning  the  wheel  with  the 

75.  Define  radius,  periphery,  and  eccentric  wheels. 

76.  What  is  a wheel  and  axle  ? 

77.  Explain  the  first  diagram. 


WHEEL  AND  AXLE. 


37 


hand,  we  wind  a rope  round  the  circumference  of  the 
wheel,  in  a contrary  direction  from  that  in  which  the  axle 
rope  is  wound,  and  also  hang  a weight  of  a certain  heavi- 
ness, P,  to  its  extremity,  then  the  draught  or  pulling  of  the 
wheel  rope  in  unwinding,  will  turn  the  axle,  and  so  wind 
up  the  axle  rope  with  its  weight.  In  this  manner,  oee 
power  works  against  another,  exactly  as  in  the  case  of  the 
lever.  By  properly  apportioning  the  two  powers  in  corres- 
pondence with  the  diameters  of  the  wheel  and  the  axle,  the 
one  power  or  weight  may  be  made  to  balance  the  other  power 
or  weight,  so  as  to  produce  an  equilibrium  of  the  machine. 

99.  The  wheel  and  axle  form  what  is  called  a perpetual 
lever.  Common  simple  levers  act  only  for  a short  space, 
or  by  reiterated  efforts,  so  as  to  be  adapted  for  lifting  an 
object  from  one  place  to  another  on  the  ground.  The 
perpetual  lever,  formed  by  the  wheel  and  axle,  turns  round 
without  intermission,  and  is  therefore  suitable  for  lifting 
weights  attached  to  a rope,  through  a considerable  space 
upward  from  the  ground  without  stopping. 

91.  Figure  31  is  a representation  of  the  machine  end- 
Figure  31.  wise,  and  shows  how  the  lever  operates. 

The  line  going  across  the  machine  from 
A to  B represents  the  line  of  the  lever. 
A is  the  situation  of  the  power,  F is  the 
centre  or  fulcrum,  and  B is  the  situation 
of  the  wmight ; therefore,  from  A to  F is 
the  long  arm,  and  from  F to  B is  the 
short  arm  of  the  lever.  In  other  words, 
the  long  arm  is  half  the  diameter  of  the 
wheel,  and  the  short  arm  is  half  the 
thickness  or  diameter  of  the  axle. 

92.  By  widening  the  wheel,  and  so 
lengthening  the  long  arm  of  the  lever,  the  smaller  will  be 
the  power  necessary  to  overcome  the  weight  on  the  axle  or 
short  arm;  but  what  is  gained  by  this  mechanical  advantage  is 
lost  by  the  circumstance  that  the  power  must  descend  through 
a proportionally  greater  space  in  order  to  raise  the  same 


78.  What  is  the  use  of  the  second  ? 

79.  How  is  this  shown  to  he  a modification  of  the  lever? 


33  WHEF.l.  AND  AXLE. 

weight  through  tlie  same  space  in  the  same  time.  This  is  in 
agreement  with  the  principle  mentioned  in  paragraph  17. 

93.  To  find  what  forces  will  balance  each  other,  let  the 
same  rules  be  followed  as  those  given  for  the  simple  lever 
in  paragraph  25.  Multiply  the  weight  by  its  distance  from 
the  fulcrum  (that  distance  is  half  the  diameter  of  the  axle;  ; 
then  multiply  the  power  by  its  distance  from  the  same  point 
(that  is,  half  the  diameter  of  the  wheel),  and  if  the  products 
be  equal,  the  weight  and  the  power  will  balance  each  other. 
Thus,  a power  of  one  pound  at  or  depending  from  the  cir- 
cumference of  a wheel  of  twelve  inches  in  diameter,  will 
balance  a weight  of  twelve  pounds  at  or  depending  from 
the  circumference  of  an  axle  one  inch  in  diameter. 

Note.  No  allowance  is  made  in  these  calculations  for  the 
overlaying  of  the  rope  in  winding,  which  affects  the  length 
of  both  the  long  and  short  arm  ; but  this  is  a matter  of  prac- 
tical, not  of  theoretic  import. 

94.  The  principle  of  the  wheel  and  axle,  or  perpetual 
lever,  is  introduced  into  various  mechanical  contrivances 
which  are  of  great  use  in  many  of  the  ordinary  occupations 
of  life.  One  of  the  simplest  machines  constructed  on  this 
principle,  is  the  common  windlass  for  drawing  water  by  a 
rope  and  bucket  from  wells.  Coal  is  lifted  from  the  pits 
in  which  it  is  dug,  by  a similar  contrivance,  wrought  by 
horse  or  steam  power. 

95.  The  capstan  in  general  use  on  board  of  ships  for 
hauling  or  drawing  up  anchors, 
and  for  other  operations,  is  an 
example  of  the  wheel  and  axle, 
constructed  in  an  upright  or 
vertical,  instead  of  a horizon- 
tal, position.  In  figure  32, 
one  of  these  capstans  is  repre- 
sented. The  axle  is  placed 
upright,  with  the  rope  windin 
about  it,  and  having  a hea 
pierced  with  holes  for  spokes 


Figure  32. 


80.  By  what  rule  are  the  forces  calculated  * 
SI.  What  examples  are  cited  1 


biro 


PULLEYS. 


33 

or  levers,  which  the  men  push  against  to  cause  the  axle  to 
turn.  This  is  a powerful  and  convenient  machine  on  ship- 
board ; when  not  in  use,  the  spokes  are  taken  out  and  laid 
aside. 

An  illustration  of  the  wheel  and  axle,  in  a combined 
form,  is  afterwards  given  in  the  case  of  the  crane. 

OF  CORDS  AND  PULLEYS. 

96  The  pulley,  or  cord,  is  one  of  the  primary  mechani- 
cal powers.  A pulley  is  a wheel,  with  a groove  in  its 
circumference,  and  is  suspended  by  a central  axis.  In  fixed 
pulleys,  a flexible  cord,  which  is  made  to  pass  over  and 
hang  from  the  upper  part  of  the  groove,  has  at  one  extremity 
a certain  weight  to  be  raised,  and  at  the  other  extremity  a 
power  is  attached  for  the  purpose  of  pulling. 

97.  There  are  two  kinds  of  pulleys,  the  fixed  and  move- 
able. 


FIXED  PULLEYS. 


A ^ 


t 


PQ 


Figure  33.  98.  The  annexed  cut,  figure  33,  repre- 

— B "~iimsents  a fixed  pulley.  A is  the  wheel ; B 
'is  a beam  or  roof  from  which  the  wheel  is 
suspended.  P is  the  power  hanging  at  one 
end  of  the  rope,  and  VV  is  the  weight  at 
the  other  end.  This  kind  of  -pulley  is 
called  a fixed  pulley,  because  it  does  not 
shift  from  its  p sition. 

99.  The  fixed  pulley  possesses  no  me- 
chanical advantage.  The  wheel  is  merely  a lever  with 
equal  arms,  and  therefore  the  cord  which  passes  over  these 
arms  gains  no  advantage.  To  raise  a pound  weight  from 
the  ground  at  the  one  end  of  the  cord,  the  power  of  one 
pound  must  be  exerted  at  the  other. 

190.  The  object  of  the  single  fixed  pulley  is  not  to  save 


6^ 


82.  Define  a pulley,  and  how  many  kinds. 

S3.  Explain  the  first  diagram. 

84.  What  advantage  is  gained  by  a fixed  pulley  > 


40 


PULLEYS. 


power,  but  to  give  convenience  in  pulling.  For  instance, 
by  pulling  downwards,  a weight  may  be  raised  upwards,  or 
by  pulling  in  one  direction,  a load  may  be  made  to  proceed 
in  another.  The  same  object  might  be  gained  by  drawing 
a cord  over  a fixed  post  or  pivot,  but  in  this  case  the  fric- 
tion of  the  cord  would  chafe  or  injure  it;  the  wheel  or 
pulley  is  therefore  a simple  contrivance  to  prevent  friction, 
for  it  turns  round  along  with  the  cord. 


MOVEABLE  PULLEYS. 

101.  The  moveable  pulley  is  in  form  the  same  as  the 
fixed  pulley,  but  instead  of  being  placed  in  a 
fixed  position  from  a beam  or  roof,  it  hangs 
in  the  cord  which  passes  under  it,  and  from 
it  the  weight  is  suspended.  In  figure  04,  a 
moveable  pulley  is  represented.  A is  a hook 
in  a beam  to  which  one’  end  of  a cord  is 

p fixed.  B is  the  moveable  pulley,  under 
L which  the  cord  passes  and  proceeds  upwards 
® to  C,  a fixed  pulley,  from  which  it  depends 
to  P,  the  power  or  the  hand  pulling.  The 
fixed  pulley  C is  of  no  further  use  than  to 
change  the  direction  of  the  power.  W is 
the  weight  hanging  from  B. 

102.  The  moveable  pulley  possesses  a mechanical  ad- 
vantage. The  first  point  to  be  observed  is,  that  the  weight 
hangs  in  the  cord  ; second,  that  the  weight  presses  down 
each  side  of  the  cord  equally — that  is,  it  draws  as  hard  at 
A as  at  C or  P ; third,  that  the  consequence  of  this  equal 
pressure,  is  the  halving  of  the  wreight  between  the  two  ends 
of  the  cord  The  halving  of  the  weight  is  therefore 
the  mechanical  advantage,  given  by  the  moveable  pulley. 

103  Example. — If  the  weight  W be  ten  pounds,  five 
pounds  is  borne  by  A,  and  five  pounds  by  P.  The  case 
is  precisely  the  same  as  that  of  two  boys  carrying  a basket 
between  them.  The  basket  is  the  weight,  and  each  boy. 


Figure  34. 


85.  Explain  the  moveable  pulley  and  the  diagram. 

86.  In  w hat  does  the  advantage  consist  ? 


PULLEYS. 


41 


with  his  hand  upholding  the  handle,  bears  only  half  the 
load,  whatever  it  may  be.  If,  instead  of  holding  by  the 
handle,  the  boys  slip  a cord  beneath  it,  and  each  take  an 
end  of  the  cord,  the  case  is  the  same. 

104.  In  order  to  save  expenditure  of  power  in  lifting 
weights  by  pulleys,  it  is  always  contrived  to  cause  some  in- 
animate object,  as  for  instance  a beam  or  roof,  to  take  a 
share  of  the  weight,  leaving  only  a portion  to  be  borne  by 
the  person  who  pulls.  But  in  this  as  in  all  cases  of  me- 
chanical advantage,  the  saving  of  power  is  effected  only  by 
a certain  loss  of  time,  or  a longer  continuation  of  labour. 
To  lift  a weight  one  foot  Horn  the  ground,  by  the  moveable 
pulley  a man  must  pull  up  the  cord  two  feet : therefore  to 
lift  a weight,  it  will  take  double  the  exertion  to  draw  it  up 
a given  height  in  a given  time  without  the  pulley,  that  it 
would  require  with  the  intervention  of  the  pulley. 

105.  As  the  power  which  a man 
can  exert  by  his  hands,  is  able  to  over- 
come a weight  greater  than  the  weight 
ol  his  own  person,  this  circumstance 
may  be  taken  advantage  of  in  a very 
peculiar  manner,  through  the  agency 
( f the  fixed  pulley.  As  represented 
in  figure  35,  a man  may  seat  himself 
in  a loop  or  seat  attached  to  one  end 
of  a cord,  and  passing  a cord  over  a 
fixed  pulley  above,  may  pull  himself 
upwards  by  drawing  at  the  other  end 
of  the  cord.  By  adding  a moveable 
pulley  and  another  fixed  pulley  to 
the  apparatus,  the  exertion  of  pulling 
would  be  diminished  one  half.  An 
apparatus  of  this  nature  having  two 
fixed  pulleys  and  one  moveable  pulley,  is  used  by  house 
masons  and  other  artizans,  in  making  repairs  on  the  fronts 
of  buildings. 


Figure  35. 


87.  What  illustrations  are  given  7 

88.  Explain  the  diagram. 

89.  How  may  the  exertion  be  diminished  7 


42 


PULLEYS. 


PRINCIPLE  OF  THE  PULLEY  POWER. 

106.  The  principle  upon  which  pulleys  act,  is  the  dis- 
tribution of  weight  throughout  the  different  portions  of  the 
cord,  so  as  to  lessen  the  power  necessary  to  be  exerted  by 
the  operator.  And  along  with  this  principle  is  the  chang- 
ing of  the  direction  of  the  power  for  the  sake  of  conveni- 
ence in  pulling. 

107.  According  to  ordinary  language,  the  mechanical 
power  of  which  we  are  treating,  is  called  the  power  of  the 
pulley;  but,  in  reality,  as  has  been  just  shown,  the  pulley 
has  no  power  in  itself.  The  power  of  the  machine  is  in  the 
cord.  It  is  the  equal  tension  of  the  cord  through  its 

WHOLE  LENGTH,  BY  WHICH  THE  WEIGHT  IS  DISTRIBUTED 
UPON  INTERVENING  POINTS,  THAT  THE  MACHINE  OFFERS 
ANY  MECHANICAL  ADVANTAGE. 

108.  In  all  cases  in  which  cords  are  drawn  tightly,  so 
as  to  hold  objects  in  close  contact,  the  same  species  of 
power  or  mechanical  advantage  is  exemplified.  For  in- 
stance, in  drawing  a cord  in  lacing,  or  a thread  in  sewing, 
this  distribution  of  power  is  observable.  If  all  the  power 
which  is  distributed  throughout  the  sewing  of  a single  pair 
of  strong  shoes,  were  released  and  concentrated  in  one  main 
draught,  it  would,  in  all  likelihood,  be  a power  sufficient  to 
lift  one  or  two  tons  in  weight. 

109.  Technically,  the  wheel  of  a pulley  is  called  a sheave; 
for  protection  and  convenience  this  sheave  is  ordinarily  fixed 
with  pivots  in  a mass  of  wood  called  a block;  and  the  ropes 
or  cords  are  called  a tackle.  The  whole  machine  fully 
mounted  for  working  is  termed  a block  and  tackle.  By 
causing  a wheel  and  axle  to  wind  up  the  cord  of  a block 
and  tackle,  the  power  of  the  lever  is  combined  with  that  of 
the  pulley  in  the  operation. 

110.  There  is  no  assignable  limit  to  the  power  which 


90.  Explain  the  principle  of  the  pulley. 

91.  Where  is  its  power  found  ? 

92.  Name  the  illustrations  of  this  power. 

93.  Define  sheave,  block  and  tackle. 

94.  What  is  said  of  the  limit  of  this  cower? 


PULLEYS  IN  COMBINATION 


43 


may  be  exerted  by  means  of  pulleys.  The  machine  may 
be  constructed  to  raise  with  ease  any  weight  which  the 
strength  of  materials  will  bear,  provided  the  combination 
is  not  so  complex  as  to  exhaust  the  power  by  the  friction 
produced. 

111.  The  power  of  pulleys  is  increased  by  a combination 
of  wheels  or  sheaves  in  one  tackle.  There  are  different 
kinds  of  combinations  or  systems  of  pulleys.  In  some  there 
is  only  one  fixed  pulley,  and  in  others  there  are  several. 


Figure  36. 


COMBINATIONS  OF  PULLEYS. 

The  following  are  examples  of  different  combinations  of 
pulleys : — 

112.  Figure  36  represents  a compound 
system  of  pulleys,  by  which  the  weight  is 
distributed  through  four  folds  of  the  same 
cord,  so  as  to  leave  only  a fourth  of  the 
weight,  whatever  it  may  be,  to  be  raised 
by  the  operator.  In  this  illustration,  the 
cord  number  1 bears  one  fourth  of  the 
weight ; the  cord  number  2 bears  a se- 
cond fourth ; the  cord  number  3 bears  a 
third  rourth  ; and  the  cord  number  4 bears 
a fourth  fourth.  Here  the  mechanical 
advantage  ceases.  For,  although  the  cord 
number  4 passes  over  the  topmost  fixed 
pulley  down  to  the  hand  of  the  operator, 
no  more  distribution  of  power  takes  place  ; 
this  topmost  pulley  being  of  use  only  to 
change  the  direction  of  the  power.  The 
p rson  who  pulls  has  hus  only  a quarter  of  the  weight  to 
diaw.  If  the  we  ght  e one  hundred  pounds,  he  has  the 
labour  of  pulling  only  twenty-five  pounds. 

113.  Thus  it  is  observable  that  the  diminution  of  weight 
is  in  proportion  to  the  number  of  moveable  pulleys.  To 


95.  How  may  it  be  increased  ? 

96.  Explain  the  first  diagram. 

97.  How  is  the  power  calculated  1 


4 i 


PULLEVS  IN  COMBINATION. 


calculate  the  expenditure  of  power  or  diminution  of  weight, 
therefore,  we  have  only  to  multiply  the  number  of  moveable 
pulleys  bv  two,  and  the  product  shows  the  power  to  be  ex- 
erted. Two  moveable  pulleys  multiplied  by  two,  gives  4 ; 
therefore  a fourth  of  the  weight  is  the  power  required,  and 
so  on.  The  addition  of  a single  moveable  pulley  to  any 
system  of  pulleys,  at  once  lessens  the  apparent  weight  one 
half,  or,  in  other  words,  doubles  the  effect  of  the  power  ; 
but  every  such  addition  causes  more  time  to  be  spent  in 
the  operation,  there  being  at  every  additional  fold  of  the 
cord  more  cord  to  draw  out,  and  also  more  friction  to 


overcome. 


Figure  37. 


pr 

1 

i i 

pi 

1 c 

2 

4 

4 

114.  In  the  annexed  system  of  pul- 
leys, figure  37,  a series  of  moveable 
pulleys,  with  different  cords,  are  made 
to  act  successively  on  one  another, 
and  the  effect  is  doubled  bv  each  pul- 
ley. At  the  extremity  of  the  first  cord 
a power  of  one  pound  depends.  This 
cord,  marked  l,  by  being  drawn  bel<  w 
a moveable  pulley,  supports  2 pounds 
— that  is  l pound  on  each  side.  The 
next  cord  marked  2,  in  the  same  man 
ner  supports  four  pounds,  or  2 pounds 
on  each  side.  The  next  cord  marked  4 
supports  eight  pounds,  or  our  potindt 
on  each  side.  Thus  1 pound  at  P,  supports  S pounds  at 
W.  If  another  moveable  pulley  were  added,  the  1 pound 
at  P would  support  Hi  pounds,  and  so  on. 

115.  In  working  pulleys,  the  power  must  be  applied  in 
a line  perpendicular  to,  or  parallel  with,  the  weight;  that 
is,  straight  above  the  weight,  in  order  to  produce  the  full 
efficacy  of  direct  force.  If  the  power  be  applied  obliquek 
— do  not  draw  fair  up — there  will  be  a loss  of  power  in 
proportion  as  the  line  of  draught  departs  from  the  perpen- 
dicular. 


98.  What  of  the  next  diagram  7 

99.  What  of  oblique  action  7 


THE  INCLINED  PLANE. 


45 


PRACTICAL  APPLICATION  OF  PULLEYS. 

116.  Pulleys  are  used  chiefly  on  board  of  ships,  where 
blocks  and  tackle  are  in  constant  requisition  for  raising 
and  lowering  the  sails,  masts  and  yards.  They  are  like- 
wise in  considerable  use  by  house-builders  and  others,  in 
connection  with  the  wheel  and  axle,  for  raising  or  lowering 
heavy  irasses  of  stone  and  other  articles. 

117.  Figure  38  is  a representation  of 
a system  of  pulleys  commonly  used  in 
practical  operations.  Three  moveable 
pulleys  are  inclosed  in  the  block  A,  and 
three  fixed  pulleys  are  inclosed  in  the 
block  B.  Suppose,  therefore,  that  the 
weight  W in  this  case,  is  six  hundred 
pounds,  the  hand  P pulls  it  upwards  by 
exerting  a force  of  only  one  hundred 
pounds.  A combination  of  pulleys  re- 
sembling this  is  used  in  turning  kitchen 
jacks.  The  weight  in  sinking  draws 
off  the  cord  from  a spindle,  by  which 
motion  the  jack  is  turned.  In  order 
that  a considerable  weight  falling  slowly 
through  a comparatively  small  height 
may  keep  the  jack  in  motion  for  a long  time,  as  many  as 
ten  or  twelve  moveable  and  fixed  pulleys  are  used. 

OF  THE  INCLINED  PLANE. 

118.  A horizontal  plane  is  a plane  coinciding  with  that 
Figure  39.  °f  the  horizbn,  or  parallel  to  it; 

when  the  plane  is  not  level  or 
horizontal,  but  lies  in  a sloping 
direction,  with  one  end  higher  than 
the  other,  it  is  said  to  incline,  or  is 
called  an  inclined  plane.  Figure 

39  is  an  example. 


Figure  38. 


100.  Name  the  uses  of  this  power. 

101.  Explain  the  diagram. 

102.  What  of  an  inclined  plane  1 


46 


STANDARD  OP  INCLINATION. 


90  80 


Insure  40. 


STANDARDS  OF  COMPARISON  FOR  INCLINATIONS. 

119.  The  inclination  of  a plane  may  be  to  any  exient, 
from  that  of  a slight  rise  off  the  horizontal  to  almost  an  up- 
right or  perpendicular  ascent.  For  the  sake  of  conveni- 
ence in  language,  the  extent  of  the  inclination  is  defined 
by  comparing  it  to  the  numbers  of  degrees  in  a quarter  of 

a circle.  A circle  being  divided  by  ma- 
thematicians into  360  degrees  or  parts, 
the  quarter  of  the  circle  includes  ninety 
degrees.  Taking,  then,  a quarter  of  a 
circle,  and  marking  it,  as  in  figure  40, 
H L is  the  horizontal  line,  and  P L is 
the  perpendicular  line  ascending  from 

it.  Any  line  drawn  from  the  centre  to 

H L any  point  on  the  circumference  defines 

the  degree  of  inclination.  Thus,  a line  ascending  from 
the  centre  to  the  10th  degree  is  called  an  inclination  or 
angle  often  degrees;  a line  ascending  to  the  45th  degree 
is  called  an  inclination  or  angle  of  forty-five  degrees  ; and 
so  on  with  all  the  other  degrees,  to  the  90th.  In  this  man- 
ner a standard  of  comparison  has  been  established  for  de- 
fining the  various  slopes  or  inclinations  in  planes. 

120.  Another  standard  of  comparison  for  slopes  consists 
in  referring  the  rise  to  so  many  feet  in  a certain  length  or 
distance — as  for  instance,  a rise  of  one  foot  in  ten  feet,  a 
rise  of  one  foot  in  twenty,  a rise  of  so  many  inches  in  a 
mile,  and  so  on. 

121.  In  the  case  of  inclinations  of  hills,  or  other  eleva- 
tions composed  of  loose  matter,  there  is  a certain  degree 
of  sloping,  which  will  permit  the  materials  to  remain  at 
rest,  and  not  slide  or  roll  down  in  obedience  to  the  law  of 
gravitation.  The  degree  of  inclination  at  which  the  parti- 
cles of  matter  remain  at  rest,  just  before  they  would  slide 
down,  is  termed  the  angle  of  repose.  This  angle  is,  of 
course,  different  in  different  kinds  of  bodies. 


103.  What  variety  of  inclined  planes  and  how  described  ? 

104.  Explain  the  diagram. 

105.  What  other  standard  is  used  ? 


THE  INCLINED  PLANE. 


47 


PRINCIPLE  OF  THE  POWER  OF  INCLINED  PLANES. 

122.  The  inclined  plane,  as  already  stated,  is  a primary 
mechanical  power.  The  object  which  is  accomplished  by 
it  is  the  raising  of  weights  to  considerable  elevations,  or  the 
overcoming  of  resistances  by  the  application  of  lesser 
weights  and  resistances ; or,  making  a small  power  over- 
come a greater. 

123.  To  raise  a load  of  a hundred  pounds  to  an  elevation 
of  fifty  feet  by  a direct  perpendicular  ascent,  and  without 
using  any  mechanical  advantage,  the  power  exerted  must 
be  a hundred  pounds,  or  equal  to  the  weights  to  be  over- 
come. If,  instead  of  raising  the  load  directly  upwards,  we 
raise  it  by  the  gradual  ascent  of  an  inclined  plane,  the  power 
required  is  less  than  a hundred  pounds,  and  the  diminution 
is  in  proportion  to  the  smallness  of  rise  in  the  inclined 
plane.  But  this  saving  of  power,  as  in  all  other  instances 
of  mechanical  advantage,  is  accomplished  only  by  a corres- 
ponding loss  of  time. 

124.  In  drawing  a load,  as,  for  instance,  a loaded  car- 
riage, along  a horizontal  plane,  the  resistance  to  be  over- 
come is  chiefly  the  friction  of  the  load  upon  the  plane.  If 
there  were  no  friction  or  impediment  from  inequalities  of 
surface,  and  if  the  load  were  once  put  in  motion,  it  would 
go  on  moving  with  the  smallest  possible  expenditure  of 
power. 

125.  In  drawing  a load  up  an  inclined  plane,  ordinary 
friction  has  to  be  overcome,  and  also  the  gravity  of  the 
body,  which  gravity  gives  it  a tendency  to  roll  down  to  the 
lowest  level.  In  this  constant  impulse  to  descend,  it  is 
not  at  liberty  to  pursue  the  same  line  of  descent  as  bodies 
falling  freely  from  heights.  It  falls  or  rolls  down  as  much 
less  speedily  than  a free  falling  body  (omitting  the  loss  by 
friction)  as  the  length  of  the  inclined  plane  is  greater  than 
its  height.  A freely  descending  body  falls  about  16  feet 


106.  What  mechanical  objects  are  thus  gained  ? 

107.  Name  the  illustration  here  cited. 

108.  What  resistance  has  to  be  overcome  ? 


43 


THE  INCLINED  PLANE. 


Figure  41. 
A 


HI 


in  the  first  second;  and  a body  rolling  down  an  inclined 
plane,  mils  just  as  many  feet  the  first  second  as  the  number 
of  feet  of  inclination  is  in  sixteen  feet.  If  the  inclination  be 
one  foot  in  sixteen,  the  body  rolls  down  one  foot,  and  so  on. 

126.  Any  body  in  being  drawn  up  an  inclined  plane,  by 
a power  parallel  with  the  plane,  presses  at  right  angles  with 
the  plane.  The  common  expression  is,  that  the  reaction 
of  the  plane  upon  the  object  is  perpendicular  to  the  plane. 

When  an  object,  as  a ball,  rests  upon  a 
horizontal  plane,  its  pressure  is  at  right 
D angles  with  the  plane  ; or  what  is  the  same 
_ thing,  the  reaction  or  resistance  of  the 
B c plane  is  at  right  angles  with  it.  This  is 
seen  in  figure  41,  in  which  a ball  is  represented  lying  on  a 

Figure  42.  level  plane,  with  the  line  of  pressure  A pass- 
ing down  to  B,  which  line  is  at  right  angles 
D with  the  plane.  Suppose,  then,  that  the  end 
of  the  plane  at  C is  elevated  to  D,  as  in 
-C  figure  42,  so  as  to  form  a slope  ; in  this  case 
the  line  of  pressure  of  the  ball  on  the  plane  is  also  moved, 
so  as  still  to  be  at  right  angles  with  the  inclination.* 

127.  The  power  which  is  required  to  be  sustained  for 
the  purpose  of  overcoming  friction  or  inequalities  of  surface 
on  level  planes,  is  for  the  purpose  of  drawing  the  load  up 
or  over  the  inequalities. 


RULES  FOR  CALCULATING  THE  POWER  OF  INCLINED  PLANES. 

128.  The  amount  of  the  power  corresponding  to  different 
weights  and  inclinations  of  the  plane  has  been  correctly 
ascertained,  and  the  following  are  the  rules  upon  the  sub- 
ject : — 

129.  First. — The  quantity  of  weight  is  great  in  propor- 
tion to  the  inclination  of  the  plane;  consequently,  so  is  the 

* This  proposition  is  proved  by  a mathematical  demonstration  which 
it  is  thought  inadvisable  to  introduce  here.  The  question  is  one  of 
Resolution  of  Forces,  and  is  treated  of  in  works  for  advanced  students. 


109.  What  of  the  ratio  of  descent  ? 

110.  Explain  the  diagrams. 

111.  How  is  the  power  of  inclined  planes  calculated  7 


THE  INCLINED  PLANK. 


49 


difficulty  of  raising  greater,  and  the  rate  of  elevation  or 
motion  slower. 

1 :30.  Second. — To  overcome  the  weight  or  resistance, 
and  the  slowness  of  movement,  a corresponding  increase 
of  power  must  be  given. 

131.  Third. — The  smaller  the  inclination,  so  is  the 
pressure  of  the  weight  on  the  plane  the  greater. 

132.  Fourth,  or  special  rule  of  calculation. — Whatever 
is  the  unit  of  inclination  in  a given  length,  the  same  is  the 
unit  of  weight  that  can  be  lifted,  and  the  unit  of  power  to 
be  exerted. 

EXAMPLES. 

133.  If  the  inclination  of  a road  be  one  foot  in  ten,  one- 
tenth  is  called  the  unit  of  inclination  ; hence,  one-tenth  part 
of  the  nominal  weight  of  the  load  has  to  be  lifted ; and  a 
power  to  draw  this  one-tenth  part  of  the  load  has  to  be 
exerted.  Or,  to  put  the  case  in  other  words  : — If  the  road 
rise  one  foot  in  ten,  there  is  in  the  ten  only  one  foot  of 
perpendicular  height  to  be  lifted  through  ; and  the  weight 
at  any  point  of  the  ten  feet  is  only  a tenth  of  what  it  would 
be  if  it  were  to  be  lifted  through  a perfect  perpendicular 
ascent  of  ten  feet.  This  is  exemplified  in  figure  13,  in 

Figure  43. 


which  a loaded  cart  is  in  the  act  of  being  drawn  up  an 
inclined  plane  of  ten  feet  in  length,  having  a rise  of  o le 
foot  throughout  its  extent,  that  is,  from  A to  B.  This  rise 
of  one  foot  is  marked  at  the  end  of  the  plane,  from  C to  R. 
Although,  therefore,  the  cart  has  to  be  pulled  a distance  of 
ten  feet,  it  in  reality  is  pulled  upwards  only  one  foot,  and 


1 12.  What  is  the  unit  of  inclination  ? 

113.  Explain  the  diagram,  and  its  principle. 


50 


THE  INCLINED  PLANE. 


the  horse  which  draws  has  the  advantage  of  pulling  only 
orie-tenth. 

134.  The  reason  is  now  perceived  why  a small  power 
overcomes  a greater  in  the  case  of  draughts  upon  inclined 
planes.  The  load  is,  as  it  were,  lifted  by  instalments. 
Partly  supported  as  it  advances,  and  always  supported  more 
completely  the  smaller  the  inclination,  the  weight  of  the 
burden  is  apparently  lessened  by  merely  taking  the  rise 
gradually  and  slowly. 

135.  If  we  suppose  a case  of  two  roads,  the  first  rising 
one  foot  in  twenty,  and  the  second  rising  one  foot  in  fifty, 
a loaded  carriage  will  be  found  to  go  over  the  fifty  feet  of 
the  one  with  precisely  the  same  expenditure  of  power  that 
would  be  required  to  make  it  go  over  the  twenty  feet  of 
the  other — that  is,  always  providing  that  friction  and  other 
circumstances  are  alike. 

136.  Figure  44  represents  a supposed  case  of  two  in- 
clined planes  of  the  same  height,  but  different  slopes,  meet- 
ing together  at  the  top,  with  a weight 
resting  on  each,  P and  Q,  hanging 
by  a string,  which  passes  over  the 
pulley  M.  If  the  length  of  the 

A B ■ longest  plane  from  A to  M be  two 

feet,  and  that  of  the  shorter  from  B to  M be  one  foot,  then 
two  pounds  at  Q,  on  the  short  side,  will  balance  four  pounds 
at  P,on  the  long  side ; and  so  on  in  this  proportion,  whether 
the  planes  be  longer  or  shorter. 

137.  In  this  manner,  weights  moving  on  two  adjoining 
inclined  planes  may  be  adjusted  so  as  to  balance  each 
other,  although  the  inclinations  be  different;  and  they  are 
so  made  to  act  on  various  sloping  railways  connected  with 
public  works,  where  one  wagon  descending  on  one  plane 
is  made  to  draw  up  another  wagon  on  another  plane. 

138.  ^n  inattention  on  the  part  of  our  forefathers  to 
these  exceedingly  simple  principles  of  mechanical  science, 
led  them  to  form  roads  over  steep  hills,  pursuing,  as  it  was 


114.  How  may  expenditure  of  power  be  estimated  1 

115.  Explain  the  first  diagram. 

116.  How  are  inclined  planes  used  on  rail  ways. 


THE  INCLINED  PLANE. 


61 


Figure  45. 


magined,the  best  routes,  because  they  were  the  straightest 
in  a forward  direction.  In  modern  times,  this  error  has 
been  avoided  by  enlight  ed  engineers,  and  roads  are  now 
constructed  with  as  few  risings  and  fallings  as  possible. 
When  roads  have  necessarily  to  be  carried  to  the  summits 
of  heights,  they  are  very  properly  made  either  to  wind  round 
the  ascent, or  to  describe  a zig-zag  line  of  direction.  Figure 
45  represents  a road  pursuing  a winding  direction  round  a 
hill  on  which  a fort  is  planted. 

139  The  drivers  of  carts  are  aware  of  the  saving  of 
labour  to  their  horses  by  causing  them  to  wind  or  zig-zag 
up  steep  roads  instead  of  leading  them  directly  forward. 

140.  The  inclined  plane  is  resorted  to  for  a saving  of 
labour  in  many  of  the  ordinary  occupations  of  life.  By  it, 
loaded  wheel-barrows  are  with  comparative  ease  wheeled  to 
considerable  elevations  in  house  building  and  other  works 
of  art ; hogsheads  are  rolled  out  of  or  into  wagpns,  and 
ships  are  launched  into  or  drawn  from  the  water,  the  in- 
clined plane  being  as  useful  in  giving  facilities  for  letting 
down  loads  as  in  drawing  them  up. 

141.  It  is  also  by  inclined  planes  that  we  reach  the 
higher  floors  of  a house  from  the  ground,  or  attain  other 


117.  Explain  the  second  diagram. 

118.  Name  some  of  the  practical  uses  of  inclined  planes. 


52 


THE  WEDGE. 


elevations.  For  all  such  purposes,  the  inclined  plane  is 
formed  with  steps  to  insure  our  safe  footing.  All  stairs  or 
flights  of  steps  are  inclined  planes.  A ladder  forms  a steep 
inclined  plane. 


Figure  46. 


OF  THE  WEDGE. 

.42.  The  inclined  plane  has  been  described  as  being 
fixed  or  stationary,  as,  for  instance,  a common  ascending 
road,  or  a sloping  plank,  upon  which  the  weights  are 
moved.  It  has  now  to  be  viewed  as  a moveable  plane,  in 
which  form  it  suits  many  useful  purposes. 

143.  When  an  inclined  plane  is  moveable,  and  the  load 
or  weight  which  it  affects  is  at  rest,  it  receives  the  name 
of  a Wedge.  The  wedge  is,  therefore,  a mechanical  power, 
founded  on  the  principle  of  the  inclined  plane. 

144.  The  Wedge  is  an  instrument  or  simple  machine, 
consisting  of  a solid  body  of  wood,  iron,  or  some 
other  hard  material,  and  is  triangular  in  form. 
See  figure  46.  Here  the  wedge  is  seen  to  taper 
from  a thick  end  or  head  at  B to  a thin  edge  or 

) point  at  A.  This,  however,  is  only  the  more 
'common  form  of  the  wedge.  It  is  made  with 
sides  of  various  angularities  or  degrees  of  slope; 
and,  in  some  cases,  it  possesses  a flat  and  a slop- 
ing side,  as  in  figure  47.  W?hen  it  slopes  on  both 
sides,  it  consists  of  two  inclined  planes  joined  together; 
Fig  47  and  when  one  of  its  sides  is  flat,  as  in  figure  47,  it 
acts  as  only  one  inclined  plane. 

145.  The  wedge  is  employed  as  an  instrument  for 
cleaving  solid  masses  asunder,  to  compress  bodies 
more  closely  together,  and  to  move  weights  through 
small  spaces.  Figure  48  is  a front  view  of  a wedge 
in  the  act  of  splitting  asunder  a piece  of  timber.  The 
power  employed  to  force  the  wedge  forward,  is  either 
repeated  blows  with  a mallet  or  hammer,  or  the  gradual 


119.  What  of  a moveable  plane  1 

120.  Explain  the  diagram. 

121.  What  of  the  varieties  and  uses  of  the  wedge. 


WEDGES. 


o) 


Figure  48  Pressure  °f  a weight.  Iii  general,  the  power 
is  applied  by  rapid  strokes,  or  quick  applica- 
tions of  some  kind  of  external  pressure. 

RULES  FOR  CALCULATING  THE  POWERS  OF  THE 
WEDGE. 

146.  The  rules  for  calculating  the  power  of 
the  wedge  are  similar  to  those  for  the  inclined 
plane.  In  proportion  as  the  inclination  or 
angularity  is  great,  so  is  the  resistance  greater,  and  I he 
power  must  be  greater  to  overcome  it.  Thus,  if  the  wedge 
be  of  short  dimensions  and  thick  at  its  head,  it  will  require 
a greater  power  to  move  it  than  if  it  be  long  and  thin  in  its 
form. 

147.  The  resistance  offered  to  the  wedge 
* gure  49,  of  equal  sides,  when  the  pressure  is  equally 
\ 7 applied,  is,  as  in  the  case  of  the  inclined 

plane,  at  right  angles  with  the  sides.  See 
\ /'^-'figure  49,  in  which  the  oblique  cross  lines 
\ / represent  the  direction  of  the  pressure  pas- 
ty sing  at  right  angles  through  the  sides,  and 

meeting  at  the  centre. 

148.  It  is  difficult  to  calculate  the  precise  power  of  the 
wedge,  for  much  depends  on  the  force  or  the  number  of 
blows  which  may  be  given  it,  together  with  the  obliquity 
of  the  sides,  and  the  power  of  resistance  in  the  object  to  be 
split  In  the  splitting  of  timber,  for  instance,  the  divided 
parts  act  as  levers,  and  assist  in  opening  a passage  for  the 
wedge. 

EXAMPLES  OF  WEDGE  POWERS. 

149.  The  wedge  is  the  least  used  of  the  simple  machines, 
but  the  principle  upon  which  it  acts  is  in  extensive  appli- 
cation. Needles,  awls,  bodkins,  and  driving-nails,  are  the 
most  common  examples.  Knives,  swords,  razors,  the  axe, 
chisel,  and  other  cutting  instruments,  also  act  on  the  prin- 


122.  By  what  rules  are  the  power  of  wedges  calculated  1 
123  What  common  examples  are  cited  1 


54 


THE  SCREW. 


ciple  of  the  wedge;  so  likewise  does  the  saw,  the  teeth  of 
which  are  small  wedges,  and  act  by  being  drawn  along 
while  pressed  against  the  object  operated  upon. 

150.  The  principle  of  the  inclined  plane,  which  is  the 
basis  of  that  of  the  wedge,  is  particularly  observable  in  ti  e 
action  of  the  razor  and  the  scythe,  both  of  which  cut  best 
by  being  drawn  along  the  materials  against  which  they  are 
applied.  When  the  edge  of  a scythe  or  razor  is  examined 
with  a microscope,  it  is  seen  to  be  a series  of  sm  ill  sh  n 
angularities  of  the  nature  of  the  teeth  of  a saw. 

Figure  50.  151.  The  principle  of  the  wedge  ope- 

rates in  the  case  of  two  glass  tumblers, 
one  placed  within  the  other,  as  in  figure 
50.  A very  gentle  pressure  applied  to  the 
uppermost  tumbler  would  be  sufficient 
to  burst  the  lower.  At  every  little  advance 
of  the  uppermost  tumbler,  it  acts  more 
and  more  as  a lever  power  on  the  rim  of 
i ;e  lower,  and  at  last  overcomes  the 
resistance,  and  fractures  the  vessel. 


OF  THE  SCREW. 

152.  The  screw  is  the  fifth,  and  usually  the  last-men- 
tioned mechanical  power.  Like  the  wedge,  it  is  founded 
on  the  principle  of  the  inclined  plane. 

Fig  51  153.  The  screw  consists  of  a projecting  ridge 

winding  in  the  form  of  an  inclined  plane,  and  in  a 
spiral  direction,  round  a central  cylinder  or  spindle, 
similar  to  a spiral  road  winding  round  a precipitous 
mountain.  Figure  51  is  a representation  of  a common 
strong  screur  used  in  various  mechanical  operations. 
The  projecting  ridge  on  the  spindle  is  technically 
called  the.  thread.  The  thread  is  not  always  made 
in  this  square  projecting  form;  it  is  frequently  sharp- 
ened to  a single  thin  edge,  as  in  figure  54,  but  this  does 
not  affect  the  principle  of  the  machine. 


124.  What  of  a microscopic  inspection  of  a razor  or  sc  vthe  ? 

125.  Explain  the  first  diagram. 

126.  What  is  the  principle  of  the  screw  ? 

127.  Explain  the  diagrams,  and  the  italicised  terms. 


THE  SCREW. 


55 


154.  One  circumvolution  or  turn  of  a thread  of  a screw 
is,  in  scientific  language,  termed  a helix  (plural  helices), 
from  a Greek  word  signifying  winding  or  wreathing,  'i  he 
spiral  winding  of  the  thread  is  called  the  helical  line. 

155.  The  helices  of  a screw  do  not  necessarily 
require  to  have  a central  spindle.  They  may  form 
a screw  of  themselves,  and  do  so  in  the  case  of  the 
i common  cork-screw.  Figure  52.  A screw  of  this 
pointed  or  tapering  form,  in  penetrating  a substance, 
possesses  the  advantage  of  the  inclined  plane  in 
three  ways;  first,  by  the  gradual  thickening  of  the 
substance  of  the  thread  from  a sharp  point ; second, 
the  gradual  widening,  and  third,  the  gradual  ascend- 
ing, of  the  thread. 


POWERS  OF  THE  SCREW. 

156.  The  screw  acts  on  the  principle  of  the  inclined 
plane,  and  this  is  obvious  from  the  consideration  of  the 
Figure  53.  nature  of  the  threads.  If  we  were  to  cut 
through  the  turns  of  the  threads  straight  from 
top  to  bottom,  and  draw  them  out  to  their  full 
extent,  each  separate  and  retaining  its  own 
inclination,  we  should  find  that  they  were  so 
many  inclined  planes.  In  the  annexed  cut, 
a figure  53,  one  entire  turn  of  the  thread  is  thus 
drawn  out,  reaching  from  b to  a,  and  is  seen  to  form  an 
inclined  plane.  If  not  drawn  out,  it  would  wind  down  to 
r ; therefore,  while  a weight  is  raised  by  one  turn  of  the 
Figure  54  screw  over  the  limits  of  one  thread,  or 
lgui-e^— ^ from  c to  b,  it  has  actually  been  carried 

Lt C — i up  the  inclined  plane  from  a to  b. 

157.  The  screw  has  no  power  by  itself. 
It  can  operate  only  by  means  of  pressure 
against  the  threads  of  another  screw 
which  overlaps  it  and  holds  it.  This 
exterior  screw,  which  is  technically  called 
a box  or  a nut,  consists  of  a block  with  a 


128.  Explain  the  first  diagram. 

129.  What  does  the  second  prove  ? 

130.  Explain  the  relation  between  the  nut  and  screw. 


50 


THE  SCREW. 


central  tube  cut  out  in  spiral  grooves  so  as  to  fit  with  perfect 
exactness  with  the  screw  which  has  to  work  in  it.  Figure 
54  represents  both  screws  in  combination.  M is  the  box  or 
nut  through  which  the  screw  passes.  L is  a lever  inserted 
into  the  head  of  the  screw,  for  the  purpose  of  turning  it. 

158.  The  object  required  by  the  use  of  the  screw  is  to 
apply  force  or  pressure.  To  produce  the  intended  effect, 
either  the  outer  or  inner  screw,  that  is,  either  the  nut  or  the 
screw,  must  be  fixed.  If  the  screw  be  fixed  at  one  ex- 
tremity, say  at  the  top,  to  a solid  body,  the  nut  may  be 
turned  round  it  so  as  to  move  from  the  bottom  to  the  top ; 
and  if  the  nut  be  fixed,  held  fast  by  some  solid  body,  the 
screw  in  the  same  manner  may  be  turned  round  till  it  reach 
its  extremity.  Thus,  either  the  point  of  the  screw,  or  the 
nut,  may  be  forced  in  such  a way  as  to  squeeze  or  press 
any  object  presented  to  them. 

159.  Practically,  the  screw  is  never  used  as  a simple 
machine  ; the  power  being  always  applied  by  means  of  a 
lever,  passing  either  through  the  head  of  the  screw,  or 
through  the  nut.  The  screw',  therefore,  acts  with  the  com- 
bined power  of  the  lever  and  inclined  plane,  and  in  investi- 
gating the  effects,  we  must  take  into  account  both  these 
simple  mechanical  powers,  so  that  the  screw  now  becomes 
really  a compound  machine. 

160.  In  the  inclined  plane,  as  has  been  seen,  the  less  it 
is  inclined,  the  more  easy  is  the  ascent,  though  the  slower 
is  the  process  of  rising  to  a certain  elevation.  In  applying 
the  same  principle  to  the  screw,  it  is  obvious,  that  the 
greater  the  distance  is  betwixt  the  threads,  the  greater  or 
more  rapid  is  the  inclination,  and, consequently, the  greater 
must  be  the  power  to  turn  it  under  a given  weight.  On  the 
contrary,  if  the  thread  inclines  downwards  but  slightly,  it 
will  describe  a greater  number  of  revolutions  in  a given 
space,  so  as  to  diminish  the  distance  betwixt  the  threads, 
and  the  smaller  will  be  the  power  required  to  turn  the  ma- 
chine under  a given  weight.  Therefore,  the  finer  the  screw, 
or  the  nearer  the  threads  to  each  other,  the  less  the  power 
will  require  to  be  for  a given  resistance. 


131.  Why  is  the  screw  called  a compound  machine  t 

132.  How  is  the  power  of  the  screw  regulated  ? 


THE  SCREW, 


57 


161.  Suppose  a case  of  two  screws,  one  having  the 
threads  one  inch  apart,  and  the  other  half  an  inch  apart; 
then,  the  force  which  the  first  screw  will  give  with  the  same 
power  at  the  lever,  will  be  only  half  that  given  by  the 
second.  The  second  sctew  must  be  turned  twice  as  many 
times  round  as  the  first,  to  go  through  the  same  space.  At 
the  lever  of  the  first,  two  men  would  raise  a weight  to  a 
given  height,  by  making  one  revolution  ; while  at  the  lever 
of  the  second,  one  man  would  raise  the  same  weight  to  the 
same  height,  by  making  two  revolutions. 

162.  It  is  apparent,  that  the  length  of  the  inclined  plane 
up  which  a body  moves  in  one  revolution,  is  the  circum- 
ference of  the  screw,  and  its  height,  the  interval  between 
the  threads.  The  proportion  of  the  power  would  therefore 
be — “ as  the  circumference  of  the  screw  is  to  the  distance 
between  the  threads,  so  is  the  weight  to  the  power.”  By 
this  rule,  the  power  of  the  screw  could  alone  be  found, 
provided  the  action  of  the  machine  was  not  affected  by  the 
lever  which  works  it.  As  that  is  the  case,  the  circumfer- 
ence described  by  the  outer  end  of  the  lever  employed  is 
taken  instead  of  the  circumference  of  the  screw  itself. 

RULES  FOR  CALCULATING  THE  POWERS  OF  THE  SCREW. 

163.  The  rule  by  which  the  true  force  of  the  screw  is 
calculated,  is,  by  multiplying  the  circumference  which  the 
lever  describes  by  the  power.  Thus — The  power  multi- 
plied BY  THE  CIRCUMFERENCE  WHICH  IT  DESCRIBES,  IS 
EQUAL  TO  THE  WEIGHT  OR  RESISTANCE,  MULTIPLIED  BY  THE 
DISTANCE  BETWEEN  THE  TWO  CON  TIGUOUS  THREADS.  Hence 
the  efficacy  of  the  screw  may  be  increased,  by  increasing 
the  length  of  the  lever  by  which  it  is  turned,  or  by  dimin- 
ishing the  distance  between  the  threads.  If,  then,  we 
know  the  length  of  the  lever,  the  distance  between  the 
threads,  and  the  weight  to  be  raised,  we  can  readily  calcu- 
late the  power;  or,  the  power  being  given,  and  the  distan  e 
of  the  threads  and  the  length  of  the  lever  known,  we  can 
estimate  the  weight  which  the  screw  will  raise. 


133.  What  illustration  is  stated  ? 

134.  How  is  the  power  calculated  ? 


58 


THE  SCREW. 


164.  Suppose  the  length  of  the  lever  to  be  forty  inches, 
the  distance  of  the  threads  one  inch,  and  the  weight  8000  ; 
required — the  power,  at  the  end  of  the  lever,  to  raise  the 
weight.  The  lever  being  40  inches,  the  diameter  of  the 
circle  which  the  lever  describes  fs  double  that,  or  80  inches. 
Reckoning  the  circumference  at  thrice  the  diameter  (though 
it  is  a little  more),  we  multiply  80  by  3,  which  gives  240 
inches  for  the  circumference  of  the  circle.  The  distance 
of  the  threads  is  one  inch,  and  the  weight  8000  pounds. 
To  find  the  power,  multiply  the  weight  by  the  distance  of 
the  threads,  and  divide  by  the  circumference  of  the  circle. 

8000  weight 
1 distance 


240)8000 

165.  Thirty-three  and  a third  is  the  product,  and  it 
would  require  that  power  or  number  of  pounds  to  raise  the 
weight.  This,  however,  is  only  in  theory.  In  practice,  a 
third  of  the  amount  of  power  would  require  to  be  added  to 
overcome  the  friction  of  the  machine. 

166.  In  the  ordinary  working  of  the  screw,  velocity  is 
incompatible  with  great  power.  This  is  a truth,  however, 
which  applies  only  to  a screw  with  one  thread.  There  is 
a way  of  making  a screw,  by  which  great  velocity  and  power 
may  be  combined.  This  is  done  by  forming  the  screw 
with  two,  three,  or  more  threads.  To  understand  ho\v  this 
is  accomplished,  we  have  only  to  conceive  the  idea  of  a 
screw  with  one  thread,  very  wide  betwixt  its  turns,  and 
then  imagine  one  or  two  other  threads  placed  so  as  to  fill 
up  the  intervals  ; thus  composing  a fine  close  screw.  And 
as  by  this  means  all  the  threads  descend  with  equal  rapidity, 
we  have  a screw  which  will  not  only  descend  with  great 
velocity,  but  which  will  apply  a very  great  degree  of  pres- 
sure. A screw  of  this  nature  is  used  in  the  printing  press, 

135.  Repeat  the  example  of  calculation. 

136.  What  of  the  friction  of  the  machine? 

137.  How  is  velocity  and  power  combined  in  a screw? 

138.  What  remarkable  instance  is  given  ? 


THE  SCREW. 


59 


by  which  a pressure  of  a ton  weight  is  applied  instanta- 
neously by  a single  pull  of  a lever. 


EXAMPLES  OF  SCREW  POWERS. 


Figure  55. 


1 

s 

1 

1 

1* 

167.  The  most  common  purpose  for  which  the  screw  is 
applied  in  mechanical  operations,  is  to  produce  great  pres- 
sure accompanied  with  constancy  of  action,  or  retention  of 
the  pressure;  arid  this  quality  of  constancy  is  always  procu- 
rable from  the  great  friction  which  takes  place  in  the  pres- 
sure of  the  threads  on  the  nut,  or  on  any  substance,  such 
as  wood,  through  which  the  screw  penetrates. 

168.  The  common  standing-press 
used  by  bookbinders  for  pressing 
their  books,  affords  one  of  the  best 
examples  of  the  application  of  the 
screw  to  produce  great  pressure.  Fi- 
gure 55.  The  screw  A lias  a thick 
round  lower  extremity  B,  into  holes 
in  which  the  lever  is  inserted.  This 
extremity  B is  attached  by  a socket 
Joint  to  the  pressing  table  C,  so  that 
when  the  screw  is  turned  in  one  direc- 
tion, the  table  sinks,  and  when 
turned  in  another,  the  table  rises. 

Jj 'The  books  D 1 le 

S,  and  are  thus  between  the  table 
and  the  sole.  H is  a cross  beam 
above,  in  which  is  the  box  or  over- 
lapping screw  to  give  the  necessary 
resistance. 

169.  The  force  of  the  screw  is 
sometimes  employed  to  turn  a wheel 
by  acting  on  its  teeth,  by  which 
means  there  is  a combination  of 
two  mechanical  powers — the  screw 
and  the  wheel  and  axle.  Figure  56.  The  screw  is  upon 

139.  What  is  the  most  common  mecha  ixal  use  of  the  screw  ? 

140  Explain  the  first  diagram. 

141.  What  combination  produces  the  e dless  screw  ? 


Figure  56. 


8 

Zjp 

8 

K|—  - 

(l 

0 } 

% 

vaN 

w 

a 

BO  MECHANICAL  COMBINATION  AND  STRUCTURE. 

the  horizontal  spindle,  and  by  turning  it  by  the  handle, 
each  turn  of  the  thread  receives  a tooth  of  the  wheel  and 
brings  it  forward,  so  as  to  produce  a perpetual  revolution 
of  the  wheel.  This  is  called  an  endless  screw,  because  it 
never  stops  in  its  action ; no  sooner  is  one  turn  of  the 
thread  disengaged  than  another  has  come  into  operation. 
W represents  a weight  to  be  raised  hanging  from  the  cir- 
cumference of  the  axle. 

170.  The  screw  concludes  the  list  of  simple  mechanical 
powers,  according  to  the  usual  definitions  of  science.  But, 
to  prevent  misconception,  it  has  to  be  noted  that  there  are 
other  means  and  agents  of  force  in  nature  besides  those 
comprehended  in  the  number  of  simple  mechanical  powers 
working  by  solids.  These  will  come  under  observation  in 
the  subsequent  departments  of  Natural  Philosophy. 

MECHANICAL  COMBINATION  AND  STRUCTURE. 

171.  Mechanical  action,  as  already  stated  (3),  is  applied 
to  the  action  of  forces  that  produce  no  change  in  the  con- 
stitution of  bodies,  and  is  therefore  distinguished  from 
chemical  or  any  other  species  of  action  in  which  change 
of  constitution  is  less  or  more  effected. 

172.  Great  changes  are  continually  taking  place  in  nature 
and  art  by  mechanical  action.  Mechanical  action  gene- 
rally implies  movement  or  change  of  place,  and  in  most 
cases  alteration  of  external  features  and  circumstances. 
The  whole  of  the  planetary  movements  are  mechanical ; 
the  motions  of  water  and  winds  are  mechanical ; and  the 
new  appearances  produced  in  art  by  placing  different  objects 
together,  are  mechanical. 

173.  The  action  of  forces  upon  solids,  or  mechanical 
action,  is  taken  advantage  of  by  mankind  for  the  produc- 
tion of  numerous  useful  results  in  the  arts.  And  success 
in  attaining  these  results  depends  in  a great  measure  upon 
the  knowledge  we  have  of  the  principles  of  Mechanics,  and 
the  skill  and  care  we  use  in  applying  them. 


142.  How  does  mechanical  action  differ  from  chemical  t 

143.  Give  instance*  of  mechanical  action. 


MECHANICAL  COMBINATION  AND  STRUCTURE. 


61 


174.  When  skill,  care,  and  ingenuity,  are  brought  fully 
into  operation  lor  these  results,  very  great  wonders  are  in 
many  instances  achieved.  But  where  there  is  ignorance 
or  negligence,  the  object  in  view  may  not  only  be  deieated, 
but  very  mischievous  consequences  may  take  place. 

175.  Example  first. — If  a tall  mast  or  beam  break 
through  at  two-thirds  of  its  height,  and  the  two  fractured 
ends  be  simply  placed  together  and  tied  with  a rope,  the 

_7  upper  piece  will,  by  the  action  of  a small  force,  again 
° fall.  It  will  act  like  the  arm  of  power  of  a lever 
against  the  rope,  which  is  the  weight ; and  as  this 
weight  is  inconsiderable,  the  arm  of  power  will  pre- 
ponderate. But  if  we  take  the  two  pieces  and  saw 
each  of  them  lengthwise,  so  as  to  make  four  pieces, 
and  then,  as  represented  in  figure  57,  lay  a short 
piece  alongside  of  a long  piece,  and  another  long 
piece  on  the  top  of  the  first  short  piece,  with  the 
second  short  piece  opposite  to  this  second  long 
piece,  the  whole  will  be  effectually  spliced  together; 
in  such  a case,  with  the  aid  of  an  overlapping  rope, 
the  beam  will  in  all  likelihood  be  stronger  than  it  was 
before  it  was  fractured.  The  cause  of  its  being  stronger, 
at  least  of  its  remaining  firm,  is,  that  the  weaker  part  at 
one  side  is  supported  by  a stronger  part  on  the  other  side. 
Thus,  by  skilfully  taking  advantage  of  certain  forces  acting 
in  connexion  with  solids,  we  are  able  to  rear  a structure  of 
the  utmost  possible  strength. 

176.  Example  second. — If  a man,  in  making  repairs 
upon  the  outside  of  a building,  project  a plank  from  a win- 
dow for  the  purpose  of  standing  upon  it,  and  if  he  proceed 
to  place  himself  near  the  outer  extremity  of  the  plank,  with- 
out having  placed  a sufficient  counterbalancing  weight  at 
its  inner  extremity,  he  will  assuredly  be  precipitated  to  the 
ground,  and  perhaps  killed  ; because  the  gravity  of  his 
body  acted  like  a power  on  the  arm  of  a lever,  while  the 
lever  was  without  a sufficient  weight  to  preserve  the  appa- 


144.  How  are  the  principles  of  mechanics  important  in  the  arts  1 

145.  Explain  the  example  and  diagram. 

146.  What  is  the  second  example  ? 


62  MECHANICAL  COMBINATION  AND  STRUCTURE. 

rntus  in  equilibrium.  From  such  neglects  of  the  operation 
of  forces  in  nature,  dreadful  consequences  frequently  ensue. 

177.  The  study  of  the  operation  of  mechanical  forces, 
along  with  experience,  teaches  that  there  are  certain  bulks, 
positions,  and  forms  of  bodies,  which  produce  the  greatest 
strength  for  purposes  of  art. 

178.  The  strength  of  beams  or  masses  of  the  same  kind 
and  bulk,  and  fixed  in  the  same  manner,  in  resisting  a 
transverse  force  which  tends  to  break  them,  is  simply  as 
their  breadth,  as  the  square  of  their  depth,  and  inversely  as 
their  length — that  is  the  thicker  and  shorter  they  are,  they 
are  the  stronger.  Thus,  if  a beam  be  twice  as  broad  as 
another,  it  will  also  be  twice  as  strong;  for  the  increase  of 
breadth  doubles  the  number  of  the  resisting  particles.  By 
making  the  beam  double  the  depth,  the  strength  is  four 
times  as  great;  because  the  number  of  fibres  is  doubled, 
and  the  lever  by  which  they  act  is  also  increased. 

179.  But  this  increase  of  strength,  by  increasing  bulk, 
has  a practical  limit.  It  is  found  that  increasing  the  di- 
mensions of  a body,  or  combination  of  bodies,  preserving 
all  proportions  the  same,  the  weight  increases  more  rapidly 
than  the  increase  of  strength,  or  power  of  endurance.  This 
is  one  of  the  most  important  principles  in  mechanical  sci- 
ence, and  ought  to  prevent  undue  extension  in  structural 
arrangements.  (39.) 

180.  Take  a block  of  stone,  and  fix  one  end  of  it  into 
a wall,  leaving  its  other  end  projecting.  By  this  arrange- 
ment of  position,  each  particle  of  matter  in  the  block  acts 
as  a weight  pulling  downwards  as  with  a lever,  the  fulcrum 
of  the  lever  being  at  the  point  of  support,  and  the  particles 
of  matter  in  the  mass  forming  at  once  the  arm  of  power 
and  the  weight.  Hence  every  particle  we  add  to  the  length 
of  the  block,  adds  to  the  length  of  the  arm  of  the  lever, 
and  increases  the  weight.  If  we  add  to  the  block  beyond 
a certain  length  (whatever  may  be  its  constitutional  strength), 
we  shall  certainly  cause  the  mass  to  break,  and  fall,  from 
the  effect  of  gravity,  upon  the  outer  extremity. 

147.  How  is  the  strength  of  beams  estimated  ? 

148  What  of  undue  extension  ?. 

149.  Cite  the  examples  here  given. 


MECHANICAL  COMBINATION  AND  STRUCTURE. 


f>3 


18 1.  A similar  lever  action  takes  effect  in  the  case  of 
blocks  or  beams  supported  at  both  ends,  the  only  difference 
being,  that,  in  extending  them  to  an  undue  length,  they 
will  break  in  the  middle,  or  at  the  weakest  point  between 
the  two  supports. 

182.  The  strength  of  a beam  supported  at  both  ends  is 
twice  as  great  as  that  of  a beam  of  half  the  length,  which 
is  fixed  only  at  one  end  ; and  the  strength  of  the  whole 
beam  is  again  increased,  if  both  ends  or  fulcra  be  firmly 
fixed,  as  into  a wall. 

183.  In  the  case  of  fibrous  or  grained  materials,  as. for 
instance,  wood,  the  body  sustains  the  greatest  pressure  when 
the  weight  is  applied  to  the  grain  endwise,  or  to  the  beam 
longitudinally.  The  nearer  that  the  pressure  can  be  ap- 
plied to  any  beam  endwise,  the  better.  Thus  a beam  sup- 
ports most  weight  on  its  upper  end,  the  other  end  being 
fixed  to  the  ground,  and  its  strength  is  next  greatest  when 
the  pressure  is  applied  to  it  leaning  at  top  against  another 
beam.  This  is  exemplified  in  the  angular  roof  of  houses, 
in  which  two  beams  lean  against  each  other  like  the  two 
sides  of  the  letter  A.  In  arranging  beams  to  support  great 
weights,  as  in  building  bridges,  each  beam  is  made  to  push 
obliquely  upward  with  one  end,  while  it  pushes  obliquely 
downward  with  the  other,  and  thus  an  extensive  combina- 
tion of  beams  is  firmly  supported. 

184.  In  rearing  structures  consisting  of  beams,  it  is  an 
important  point  to  convert,  as  far  as  possible,  by  mode  of 
erection,  cross  or  transverse  strains  into  longitudinal  strains 
or  into  forces  acting  on  the  ends  of  beams,  in  the  direc- 
tion of  their  length. 

185.  Nature  appears  to  have  designed  that  strength  of 
structure  should  be  accomplished  with  the  least  expenditure 
of  material.  It  is  obvious,  that,  if  trees  and  animals  were 
made  many  times  larger  than  we  now  find  them,  and  of  the 
same  kinds  of  substance,  they  would  be  borne  down  by 
their  own  weight.  Small  animals  endure  greater  compar- 
ative violence,  and  perform  greater  feats  of  strength,  in  pro- 


150.  What  rules  are  given  in  using  fibrous  materials  1 

151.  What  is  said  of  trees  and  animals  ? 


04  MECHANICAL  COMBINATION  AND  STRUCTURE. 

portion  to  their  size,  than  large  ones,  The  largest  bulk 
which  a human  being  can  possess  in  his  person,  at  the 
same  time  retaining  activity  of  motion,  is  not  more  than  is 
usually  seen  in  well-grown  men.  Thus,  from  a simple  na- 
tural cause,  men  of  very  gigantic  figure  never  could  have 
existed  on  our  earth.  Men  must  always  have  been  about 
the  size  which  they  are  at  present ; or,  if  they  were  con- 
siderably larger,  they  must  have  been  constituted  of  much 
stronger  materials,  without  a corresponding  increase  of 
weight. 

Iritj.  The  same  principles  relative  to  mechanical  strength 
apply  to  contrivances  in  the  arts.  As  already  stated,  the 
strength  or  power  of  endurance  in  a material  does  not  in- 
crease in  proportion  as  the  weight  increases.  Hence  there 
is  a practical  limitation  of  the  magnitude  of  machines  and 
other  structures.  For  example,  a bridge  or  roof  of  beams 
may  be  very  strong  when  of  small  or  moderate  size,  but  if 
the  dimensions  be  extended  beyond  a certain  limit,  the  struc- 
ture will  fall  by  not  beitig  able  to  support  its  own  weight. 

187.  The  strength  or  power  of  endurance  of  pressure 
upon  a fixed  body,  is  greatly  increased  by  giving  the  body 
a certain  form.  The  strongest  form  in  nature  or  art  is  that 
of  an  arch. 


ARCHED  STRUCTURES. 

188.  An  arch  is  a skilful  disposition  of  parts,  forming  a 
convex  and  concave  side,  the  convex  side  being  that  upon 
which  the  pressure  is  applied.  The  arch,  which  takes  its 
name  from  arcus,  a Latin  word  signifying  a bow,  may  be 
either  a portion  of  a circle  or  ellipse,  or  entirely  rounded 
in  form.  Whether  shaped  like  a bridge,  a round  tube,  or 
the  shell  of  an  egg,  the  principle  which  causes  the  power 
of  endurance  of  pressure  is  the  same. 

189.  The  principle  of  endurance  consists  in  the  particles 
of  the  arched  body  bearing  upon  each  other  like  a series  of 


152.  Why  is  it  certain  that  giant  stories  are  fabulous? 

153.  What  of  the  proportion  between  material  and  strength  \ 

154.  Which  is  the  strongest  form  in  nature  or  art  ? 

155.  Define  an  arch,  with  examples  of  their  variety. 


MECHANICAL  COMBINATION  AND  STRUCTURE.  65 


wedges,  thus  causing  a compression  of  particles  on  the 
concave  side  of  the  circle,  which  enables  the  mass  to  bear 
an  enormous  pressure  on  the  convex  side.  Indeed,  the 
greater  the  pressure  is  (to  a certain  extent),  perpendic- 
ular to  the  convexity,  so  also  the  compression  and  power 
of  resistance  become  the  greater. 

190.  In  the  case  of  arched  objects  which  have  to  meet 
resistance  on  all  sides,  the  circular  form  is  best.  In  the 
case  of  objects  such  as  arches  of  bridges,  which  are  ex- 
posed to  pressure  chiefly  on  one  side,  the  semicircular  form 
is  the  strongest,  or  offers  the  greatest  resistance.  The  more 
that  the  figure  of  an  arch  departs  from  the  true  circle  or 
semicircle,  the  weaker  it  becomes. 

191.  In  arched  forms  such  as  tubes  or  egg-shells,  the 
compression  of  particles  takes  place  all  round  the  inside  of 
the  object,  so  that  the  arch  presents  a power  of  resistance 
at  any  part  of  its  convexity  ; the  power  being  always  great- 
est where  the  convexity  is  greatest.  For  example,  it  is 
more  difficult  to  break  an  egg  by  pressing  against  the  two 
ends  than  against  the  sides. 

192.  In  the  representation  of  a regular-sided  wedge, 
figure  58,  to  which  the  side  pressures  are  applied  at  right 

angles  to  the  sides,  it  is  seen  that  the  lines 
of  direction  of  the  two  forces  or  pressures 
proceed  obliquely  to  a point  within  the 
wedge.  The  same  principle  applies  to  the 
particles  or  blocks  composing  arches — the 
pressing  forces  meet  in  a point  within  the 
particles  or  blocks,  and  the  situation  of  this 
p >int  is  governed  by  the  degree  of  convexity  of  the  arch, 
that  is,  the  degree  of  inclination  of  the  respective  wedges. 

193.  Hollow  cylindrical  tubes,  shafts,  pillars,  or  other 
objects  of  art,  are  much  stronger  than  the  same  objects 
would  be  if  solid,  with  the  same  quantity  of  material. 
Plates  of  metal  bent  into  grooves  on  the  surface,  are  simi- 
larly much  stronger  than  the  same  plates  when  flat.  This 


Figure  58. 


156.  Explain  the  principle  of  its  strength. 

157.  How  illustrated  by  an  egg. 

158.  Explain  the  diagram. 


66  MECHANICAL  COMBINATION  AND  STRUCTURE. 


is  well  exemplified  in  the  roofing  of.  the  large  warehouses 
and  wharfs  at  the  London  Docks,  which  are  covered  with 
sheets  of  iron.  The  sheets  are  thin  in  substance,  but  bent 
into  semicircular  grooves  and  ridges,  and  have  all  the 
strengtli  of  thick  plates  without  their  dangerous  weight. 

194.  In  arched  forms  such  as  bridges,  in  which  there  is 
only  part  of  a circle  or  ellipse,  the  two  extremities  of  the 
arch  must  rest  against  immoveable  piers  or  abutments, 
sufficiently  strong  to  resist  the  horizontal  thrust  upon 
them ; for  it  is  upon  these  parts  of  the  structure  that  the 
pressure  takes  effect. 


Figure  59. 


195.  Figure  59 
represents  the  sim- 
ple elements  of  two 
arches.  B is  an 
outer  pier,  fixed 
firmly  on  the  ground.  F is  another  pier,  and  betwixt  the 
two  there  are  two  wedge-shaped  stones,  E and  D,  lying 
obliquely  to  each  other.  It  is  obvious  that  the  more  these 
two  stones  press  downwards,  they  will  more  firmly  sustain 
each  other.  The  pier  F serves  as  a prop  to  the  other  arch, 
which  consists  of  G H I,'  and  is  supported  at  the  other  ex- 
tremity by  the  fixed  pier  K.  The  three  stones  in  this  arch 
press  against  each  other  in  the  same  manner  as  in  that  with 
the  two  stones;  and  the  same  principle  operates,  although 
the  arch  consists  of  fifty  or  a hundred  stones.  The  central 
stone  of  all  arches  is  the  stone  which  binds  the  mass  toge- 
ther, as  in  the  case  of  H,  in  the  figure,  and  is  technically 
called  the  key-stone.  It  is  always  the  last  inserted. 

196.  A.  similar  action  of  mutual  pressure  to  preserve 
equilibrium,  occurs  in  all  arched  forms.  The  human  .oot 
is  an  arch  consisting  of  small  bones  bearing  on  each  other, 
at  once  to  give  strength,  lightness,  and  elasticity. 

197.  Anciently,  bridges  were  built  of  a purely  semicir- 
cular form,  giving  a considerable  convexity  or  rise  in  the 


159.  What  example  of  grooved  material  is  g wen  ? 

160.  Where  is  the  pressure  in  arched  bridges  1 

161.  Explain  the  diagram. 

162.  What  of  the  human  foot  ? 


MACHINERY. 


t>7 

middle.  This  was  an  inconvenient  form  for  a bridge. 
Architects  now  make  bridges  with  elliptical  or  slightly 
curved  arches,  so  that  the  passage  above  them  is,  in  most 
cases,  as  easy  as  along  a piece  of  ordinary  road.  Although 
these  modern  slightly  curved  arches  are  notstrictly  so  strong 
as  a perfect  semicircular  arch,  they  are  sufficiently  durable 
for  ail  necessary  purposes.* 

ELEMENTS  OF  PRACTICAL  MACHINERY. 

198.  The  term  machine  is  ordinarily  applied  to  any  piece 
of  mechanism,  or  engine,  in  which  different  parts  are  com- 
bined to  produce  the  desired  effect.  In  Natural  Philos- 
ophy, a machine  of  this  composite  nature  is  called  a com- 
plex machine  (4). 

199.  The  treatment  of  the  principles  on  which  complex 
machines  operate,  forms  the  subject  of  the  department  of 
Natural  or  Mechanical  Philosophy  termed  Practical 
Machinery. 

These  principles  are  now  to  be  defined. 

200.  The  simple  mechanical  powers  compose  the  ele- 
ments of  all  machines,  however  complex  or  extensive.  Thus, 
in  all  machines,  levers,  cords,  or  inclined  planes,  in  their 
different  modifications,  are  found  to  be  the  elementary  com- 
ponent parts  of  the  structure,  and  all  combined  in  harmo- 
nious union  to  accomplish  certain  results. 

201.  Machines  are  usually  formed  of  wood,  iron,  steel, 
brass,  or  other  durable  materials,  with  sometimes  leather 
and  cordage  as  part  of  the  apparatus. 

202.  In  the  construction  of  every  machine,  four  objects 
are  particularly  desirable — 1st,  Strength  or  durability  of 
materials;  2d,  Simplicity  of  arrangement  of  parts;  3d,  Ex- 
actness of  fitting  of  one  part  to  another;  and  4th,  Easiness 

* A further  consideration  of  the  subject  of  strength  of  materials  be 
longs  to  Practical  Mathematics. 


163.  What  improvement  is  there  in  modern  bridges  ? 

164.  Define  a complex  machine. 

165.  What  powers  are  combined  in  their  structure  I 

166.  What  four  objects  are  sought  in  machines  1 


08 


M WHINF.R  Y. 


and  correctness  of  motion.  It  is  a general  and  well-recog- 
nized principle  in  mechanics,  that  the  fewer  the  ports  are  in 
a machine,  and  the  more.  simple  its  construction,  the  better. 

203.  Machines  act  from  the  impression  of  a certain  power 
or  force  communicated  to  them.  Whatever  be  the  amount 
of  power  they  receive,  that  amount  they  expend  in  their 
action.  They  cannot  in  the  smallest  degree  increase  the 
power.  They  can  only  convey,  regulate  and  distribute,  the 
quantity  of  power  which  has  been  communicated  to  them. 

204.  The  power  communicated  to  machines  is  derived 
from  various  sources;  as,  human  labour,  the  power  of 
horses  or  other  animals,  the  force  of  wind,  water,  or  steam, 
or  any  other  active  agent,  which  may  be  found  suitable. 
Sources  of  power  are  technically  called  moving  forces  or 
first  movers. 

205.  Of  the  original  impressed  power,  each  moving  part 
of  the  machine  uses  a certain  portion.  If  the  whole  power 
which  enters  a machine  be  supposed  to  consist  of  1000 
parts,  this  large  quantity  is  dispersed  in  various  small  quan- 
tities through  the  mechanism;  some  wheels  taking  perhaps 
10  parts,  others  5 parts,  a third  kind  1 part,  a fourth  a frac- 
tional part,  friction  another  part,  and  so  on,  till  the  whole 
1000  parts  are  expended.  In  some  large  cotton,  flax,  or 
silk  spinning  establishments,  a single  water-wheel  or  steam- 
engine  turns  several  thousands  of  spindles;  each  spindle, 
consequently,  consumes  a minute  fraction  of  the  originally 
impressed  power. 

206.  Whatever  be  the  nature  of  the  moving  forces,  it  is 
generally  sufficient  for  all  purposes  that  they  produce  in  the 
first  instance  rotary  or  circular  motion,  and  either  in  a ho- 
rizontal or  vertical  direction.  It  is,  however,  indispensable 
that  the  power  be  of  that  magnitude  which  will  cause  each 
part  of  the  machine  to  fulfil  its  assigned  office.  If  the  power 
be  too  small  or  weak,  the  machine  will  move  languidly  and 
ineffectually;  and  if  too  great,  it  will  either  cause  the  ma- 


167.  What  moving  forces  are  employed  1 
16S.  How  is  the.  power  divided  ? 

169.  What  illustration  is  cited  ? 

170.  What  motion  is  desirable  ? 


MACHINERY. 


m 

chine  to  move  too  rapidly,  or  at  least  power  will  be  expend- 
ed uselessly.  In  the  application  of  moving  forces,  it  is 
always  a matter  of  importance  to  regulate  the  power  to  the 
precise  wants  of  the  machinery. 

207.  The  circular  motion  communicated  in  the  first  in- 
stance to  a machine,  is,  by  means  of  certain  contrivances, 
diffused  through  the  whole  organization,  and  changed  into 
every  conceivable  direction  ; some  parts  being  caused  to 
revolve,  others  to  rise  and  fall,  a third  kind  to  move  hori- 
zontally to  and  fro,  and  so  forth,  in  all  possible  ways.  The 
various  parts  may  also  be  made  to  move  with  any  degree 
of  velocity  ; there  being  methods  of  transforming  quick  into 
slow  motion,  or  slow  motion  into  quick.  Most  minute  and 
complex  operations  are  thus  performed  by  machines  with  a 
precision  which  often  exceeds  the  skill  of  the  most  expert 
artizan,  but  these  operations  are  all  necessarily  marked  by 
the  quality  of  uniformity  of  action.  As  machines  cannot 
reason,  or  act  arbitrarily  in  stopping,  moving,  or  altering 
their  process,  according  to  circumstances,  they  proceed  in  a 
blind  routine,  whether  right  or  wrong,  mechanically  as  it  is 
called,  and  in  every  case  less  or  more  require  the  super- 
intendence of  reasoning  beings.  This  apparent  defect, 
however,  is  really  advantageous.  A machine  by  being 
composed  of  inanimate  matter,  destitute  of  feeling  and 
unsusceptible  of  fatigue,  proceeds  unswervingly  in  its  as- 
signed duty,  and  may  be  forced  to  accomplish  tasks  which 
it  would  be  both  inhuman  and  impolitic  to  demand  from 
living  creatures. 

20S.  The  purpose  of  machinery,  therefore,  is  to  lessen 
and  aid  human  labour.  At  an  inconsiderable  expense,  and 
with  a small  degree  of  trouble  in  supervision,  a machine 
may  be  made  to  do  the  work  of  ten,  fifty,  or  perhaps  as 
many  as  five  hundred  men  ; and  the  work  so  simply  effected 
by  inanimate  mechanism,  serves  to  cheapen  and  extend  the 
comforts  and  luxuries  of  life  to  the  great  body  of  the  people. 

The  following  are  the  chief  elementary  parts  of  machi- 
nery ; — 


171.  What  of  conformity  of  action  and  how  obtained  ? 

172.  What  is  the  great  purpose  of  machinery  ? 


WHEELS  AND  PINIONS. 


/( 


WHEELS. 

239.  A wheel  moving  on  a central  axis  is  a lever  with 
equal  arms  radiating  from  the  fulcrum  at  the  centre,  and  is 
thus  called  a perpetual  lever. 

210.  Wheels  may  be  used  in  machines  simply  to  trans- 
mit power  from  one  point  to  another.  This  is  done  by 
means  of  toothed  wheels.  Projecting  teeth  or  cogs  are 
placed  all  round  the  circumference  of  a wheel,  and,  when 
the  wheel  is  turned,  these  teeth  work  upon  or  press  against 
the  teeth  of  another  wheel,  and  so  cause  it  to  turn  also,  but 
in  an  opposite  direction.  Figure  60  represents  twro  wheels 

so  working  upon  each  other. 
As  both  of  these  wheels  are  of 
the  same  size,  and  consequent- 
ly are  levers  with  equal  arms, 
they  do  not  alter  the  effect  of 
the  power  communicated  to 
them.  The  motion  of  the  axle 
in  the  wheel  B is  the  same  as 
the  mo'ion  of  the  first  axle  in  the  wheel  A.  Thus,  power 
may  be  transmitted  from  one  point  to  another. 

211.  A long  and  large  axle,  in  wheel-work,  is  called  a 
shaft,  and  shafts  of  small  dimensions  are  termed  spindles. 
The  terminating  points  of  axles,  shafts,  and  spindles,  where 
they  rest  and  turn  upon  supports,  are  called  their  pivots  or 
gudgeons.  The  sockets  upon  which  the  gudgeons  bear  in 
turning,  are  sometimes  termed  bushes. 

WHEELS  AND  PINIONS, 

212.  When  power  has  to  be  accumulated 
p or  increased  in  its  effect  in  the  course  of  its 
transmission,  a large  wheel  is  made  to  play 
upon  a small  wheel,  by  which  means  there  is 


173.  How  do  we  obtain  a perpetual  lever  ? 

174.  How  is  power  transmitted  1 

175.  Explain  the  first  diagram,  and  the  italicised  terms. 

176.  How  is  power  accumulated  ? 


Figure  61. 


Figure  60. 


WHEELS  AND  PINIONS. 


71 


n diversity  in  the  lengths  of  the  levers.  Figure  61  is  a repre- 
sentation of  a large  wheel  YV,  working  on  a small  wheel  or 
pinion  P The  wheel  is  turned  by  the  handle  C.  In  all 
arrangements  in  which  large  wheels  are  moved  by  small 
wheels,  or  small  wheels  by  large,  the  small  wheels  are  called 
pinions  ; and  when  these  pinions  are  broad  in  their  dimen- 
sions, they  are  termed  trundles. 

213.  In  this  combination  of  a wheel  and  pinion,  a long 
perpetual  lever  works  against  a short  perpetual  lever,  by 
which  a considerable  mechanical  advantage  is  gained.  The 
wheel  may  be  supposed  to  possess  48  teeth  and  the  pinion 
6 teeth ; hence  by  one  revolution  of  the  wheel,  the  pinion 
turns  8 times,  which  gives  the  axle  of  the  pinion  eight 
times  the  velocity  of  the  axle  of  the  w heel ; and  if  we  sup- 
pose that  the  diameter  of  the  wheel  is  ten  times  the  diame- 
tc  r of  the  pinion,  the  power  is  increased  in  effect  ten  times. 

214.  Any  degree  of  velocity  greater  than  that  of  the  first 
rotary  motion,  may  be  imparled  to  the  parts  of  a machine, 
by  making  these  parts  so  much  smaller  than  the  primary 
moving  parts.  Thus,  if  a large  wheel,  having  a thousand 
teeth  in  its  circumference,  work  upon  and  turn  a small 
wheel  having  only  ten  teeth  in  its  circumference,  the  small 
wheel  will  go  round  one  time  for  every  ten  teeth  of  the 
large  wheel  which  it  touches;  or,  in  other  words,  it  wil  1 go 
round  one  hundred  times  for  one  time  of  the  large  wheel. 

The  respective  velocities 
of  wheels  in  a machine 
are,  in  this  manner,  al- 
ways proportionate  to 
their  diameters,  or  size, 
unless  when  specially  ar- 
ranged to  be  otherwise. 

2 15.  A combination  of 
wheels  acting  as  perpetu- 
al levers,  is  represented 
in  figure  62.  Three 
wheels  are  placed  in  a 


177.  What  example  is  given  ? 

178.  How  is  velocity  indefinitely  increased  ? 

179.  Explain  the  diagram  and  its  principles. 


72 


WHEELS  AND  PINIONS. 


row  close  to  each  other,  and  it  is  supposed  they  are  fixed  bv 
three  axles  to  some  upright  object.  On  the  side  of  the  first 
wheel  A,  there  is  attached  a small  toothed  pinion  or  wheel 
F,  which,  by  the  pressure  of  its  teeth  on  the  teeth  of  the 
second  wheel  B,  causes  this  second  wheel  to  turn  round. 
The  power  applied  to  produce  this  motion  is  at  the  circum- 
ference of  the  first  wheel  at  D.  From  D then,  to  the  centre 
of  the  pinion  E,  is  the  long  arm  of  a lever,  of  which  the 
centre  of  the  pinion  is  the  fulcrum;  and  from  the  centre 
to  the  ends  of  the  teeth  of  the  pinion  is  the  short  arm.  The 
second  wheel  B having  received  its  motion,  the  toothed 
pinion  G,  which  is  similarly  attached  to  its  side,  presses 
against  the  teeth  of  the  third  wheel  C,  and  so  causes  it  also 
to  turn.  In  this  way  a second  lever  is  put  in  action.  And  the 
third  wheel,  from  its  circumference  to  the  point  from  which 
the  weight  VV  depends,  is  a third  lever.  As  the  power  or 
small  weight  P falls,  therefore,  from  the  circumference  of 
the  first  wheel,  the  resistance  VV  is  raised,  with  the  accumu- 
lated force  of  three  levers  acting  on  each  other.  The  line 
across  the  figure  represents  the  three  levers  in  action. 

216.  To  calculate  the  power  or  mechanical  advantage  to 
be  gained  by  such  a machine,  suppose  the  number  of  teeth 
on  the  first  wheel  to  be  six  times  less  than  the  number  of 
those  on  the  circumference  of  the  second  wheel,  then  the 
second  wheel  would  turn  round  only  once,  while  the  first 
wheel  turned  six  times.  And,  in  like  manner,  if  the  number 
of  teeth  on  the  circumference  of  the  third  wheel  be  six 
times  greater  than  those  on  the  axle  of  the  second  wheel, 
then  the  third  wheel  would  turn  once,  while  the  second 
wheel  turned  six  times.  Thus,  the  first  wheel  will  make 
66  revolutions,  while  the  third  wheel  makes  only  one.  The 
diameter  of  the  first  wheel  being  three  times  the  diameter 
of  the  axle  of  the  third  wheel,  and  its  velocity  of  motion 
being  36  to  1,  three  times  36  will  give  the  weight  which  a 
power  of  1 pound  at  P will  raise  at  \V.  Three  times  36 
being  108,  one  pound  at  Pwill  balance  108  pounds  at  W .* 

* In  some  works,  the  product  of  the  force  multiplied  by  the  arm  of 
the  lever  with  which  it  acts,  is  technically  called  its  moment — as  “ the 
moment  of  the  power,”  “ the  moment  of  the  weight.” 

179.  How  is  its  power  calculated  t 


THE  CRANE. 


73 


PRACTICAL  EXAMPLES. 

217.  Figure  63  is  a representation  of  a machine  called 
a crane,  which  is  in  very  common  use  for  lifting  heavy 
Figure  63.  weights.  This  machine  af- 

fords a good  practical  example 
of  a combination  of  wheels  or 
perpetual  levers,  acting  so  as 
to  transmit  and  accumulate 
power.  Two  levers  operate 
in  the  machine;  the  first  arm 
is  from  the  handle  to  the  axle 
of  the  first  or  small  wheel ; 
the  second  arm  is  this  first 
wheel  from  its  axle  to  its 
toothed  circumference;  the 
third  arm  is  the  second  or 
large  wheel  from  its  toothed 
circumference  to  the  centre  of  its  axle,  and  the  fourth  arm 
is  the  radius  of  the  axle.  By  turning  the  handle,  the  first 
wheel  is  turned,  which  gives  motion  to  the  large  wheel, 
which  causes  the  axle  of  the  large  wheel  to  warp  up  the 
chain  which  is  seen  proceeding  from  it.  Thus,  any  heavy 
weight  attached  to  the  hook  at  the  outer  extremity  of  the 
chain  is  lifted.  Here,  then,  the  advantage  of  two  lever 
powers  is  brought  into  operation,  or  concentrated  upon  the 
weight  attached  to  the  hook.  The  machine  possesses  two 
handles  working  on  one  axle,  so  that  two  men,  if  necessary, 
may  work  at  it.  But  there  is  a way  of  adding  power  without 
using  two  handles.  This  consists  in  giving  the  machine 
another  wheel.  This  additional  wheel  is  placed  between 
the  small  and  large  wheel,  so  as  to  afford  another  lever 
power.  In  this  manner,  we  may  go  on  adding  wheels,  till 
at  length  the  touch  of  a finger  is  sufficient  to  raise  a ton 
weight.  But,  as  already  often  mentioned,  this  advantage 
is  procured  only  by  a loss  of  time  or  speed.  In  usual  cir- 


180.  Explain  the  diagram. 

181.  What  precaution  is  necessary  in  toothed  wheels  ? 


74 


TOOTHED  WHEELS. 


cumstances,  the  labour  of  one  or  two  men  is  employed, 
which  gives  sufficient  speed  in  the  operation. 

218.  The  crane,  as  we  have  represented  it,  is  strongly, 
but  elegantly,  constructed  of  iron.  Standing  on  the  ground 
upon  a pivot,  it  may  be  turned  about  to  any  side,  so  as  to 
bring  the  hook  over  a cart,  or  over  a vessel  from  a wharf, 
with  the  smallest  trouble.  This  conveniency  in  construc- 
tion causes  it  to  be  extensively  used  in  shipping  operations 
at  wharfs. 


Figure  64. 


WOIt KING  OF  TOOTHED  WHEELS. 

219.  In  the  working  of  toothed  wheels  one  upon  another, 
or  of  wheels  working  on  pinions,  it  is  essentia]  to  set  them 
in  opposition  with  such  exact  adjustment,  that  the  teeth  of 
one  will  fall  into  the  hollows  betwixt  the  teeth  of  the  other. 
When  the  teeth  of  each  do  not  work  with  this  nicety,  they 
are  apt  to  jar  upon  and  break  each  other,  and  so  damage 
the  machine.  In  some  cases  teeth  are  made  of  a round  or 
pointed  form  at  their  extremities,  by 
which  a very  small  degree  of  grind- 
ing or  pressing  on  each  other  takes 
place.  Figure  64  is  an  example  of 
a wheel  and  pinion  with  rounded  and 
pointed  teeth.  From  the  centre  of 
the  axis  of  the  pinion  L to  the  centre 
of  the  wheel  C,  a dotted  line  is  mark- 
ed, called  by  mechanics  the  line  of 
centres.  The  dotted  circle  O O 
round  the  pinion,  and  the  dotted 
circle  P P round  the  wheel,  indicate 
the  true  point  of  working  or  contact 
of  the  teeth  upon  each  other.  These  two  circles  are  seen 
to  join  with  exactness  at  A. 


ALTERING  THE  DIRECTION  OF  MOTION. 

220.  Motion  often  requires  to  be  altered  in  its  direction 
in  the  course  of  its  transmission.  For  example,  rotary 


1S2.  Explain  the  diagram. 

183.  What  of  altering  the  direction  of  motion  ? 


BEVEL  WHEELS  AND  BELTS. 


75 


horizontal  motion  requires  to  impart  rotary  vertical  motion, 
or  rotary  vertical  motion  to  impart  horizontal  motion.  By 
means  of  a peculiar  mode  of  setting  the  wheels,  and  a cor- 
responding peculiarity  in  the  shape  of  their  teeth,  any 
alteration  may  be  effected  in  the  direction  of  the  motion. 

221.  Figure  65  represents  a plan  of 
^ changing  the  direction  of  motion.  A 
is  a pinion  or  trundle  working  with  its 
\J  shaft  horizontally  on  a wheel  B,  whose 
16  shaft  is  turning  vertically.  As  the  case 
may  happen  to  be,  the  horizontal  move- 
ment is  causing  the  vertical  movement, 
or  the  vertical  movement  is  causing  the  horizontal  move- 
ment. 


BEVEL  WHEELS. 


Figure  66. 


222.  Figure  66  represents  a more 
common  plan  of  changing  the  direction 
of  motion.  The  wheels  in  this  case  are 
bevelled.  A bevel  wheel  is  a wheel  with 
teeth  placed  in  a sloping  or  oblique  di- 
rection on  its  circumference.  When 
two  bevel  wheels  are  placed  at  right 
angles  with  each  other,  their  respective 
teeth  work  against  each  other,  and  so  a 
harmonious  joint  motion  ensues.  This 
is  exemplified  in  the  figure,  in  which  a 
horizontal  shaft  with  a bevel  wheel,  is 
seen  turning  a smaller  bevel  wheel  above  it,  placed  on  a 
vertical  shaft. 

TRANSMISSON  OF  POWER  BY  BELTS. 


223.  A common  plan  of  transmitting  power  from  one 
point  to  another,  when  the  interval  is  considerable,  is  by  a 
flat  leather  band,  strap,  or  belt,  communicating  from  a wheel 
at  the  source  of  power  to  a wheel  connected  with  the  ma- 
chine. 


135.  Explain  the  first  diagram. 

186.  What  of  bevel  wheels? 

187.  What  other  mode  of  transmitting  power  T 


7G 


TRANSMISSION  OF  POWER  BY  BELTS. 


224.  The  wheels  upon  which  straps  work  are  usually 
called  pulleys.  They  have  flat  and  broad  rims,  and  these 
rims  have  sometimes  narrow  ledges,  to  prevent  the  belt 
from  slipping  off.  The  rims  must  also  be  rather  rough  on 
their  surface,  so  as  to  give  the  belt  a sufficient  friction  or 
power  of  pulling  in  performing  its  revolutions. 

225.  Figure  67  represents  the  transmission  of  power  by 
a belt.  A is  the  first  pulley,  which  has  received  the  power 


Figure  67. 


from  its  source,  and  C is  the  se- 
cond pulley,  moved  by  a belt, 
which  passes  over  both  pulleys. 
In  this  case  the  motion  of  A is 
transmitted  by  the  belt  to  C. 
which  it  causes  to  turn  in  the 
same  direction  as  A.  If  these  two  pulleys  were  of  precisely 
the  same  diameter,  and  th  1 belt  did  not  relax  or  slip,  the 
second  pulley  would  unavoidably  go  at  the  same  velocity  as 
the  first,  because  the  belt  has  exactly  the  property  of  a 
toothed  wheel,  and  simply  transmits  the  power  it  has  ac- 
quired. As  C appears  to  be  somewhat  smaller  than  A,  it 
would  consequently  turn  more  frequently  than  A ; there- 
fore, we  have  here  an  example  of  the  mode  of  increasing 
the  velocity  while  transmitting  power. 

226.  Figure  68  is  a representation  of  two  pulleys  moving 
in  different  directions  by  means  of  a belt.  The  large  pul- 


Figure  63. 


ley  is  supposed  to  be  that  which  has 
received  its  power  from  its  source. 
The  belt  after  leaving  it,  is  crossed, 
and,  therefore,  it  causes  the  smali 
pulley  to  move  round  in  a direction 
opposite  from  that  of  the  first.  Here, 
also,  the  second  pulley  is  smaller  than  the  first,  and  there- 
fore moves  with  an  increased  rotary  velocity. 

227.  Crossing  the  belt  serves  two  purposes.  It  changes 
the  direction  of  the  rotary  motion  which  is  sometimes  re- 
quired in  machinery,  and  causes  the  belt  to  move  more 
steadily.  When  the  belt  is  long,  it  is  apt  to  vibrate  consid- 


1S8.  Explain  the  first  diagram. 
189.  Explain  the  last  diagram. 


SHAFTS  AND  PULLEYS. 


77 


erably  in  its  motion,  from  its  weight  being  unsupported  at 
the  centre. 

228.  Power  might  be  transmitted  to  any  distance  by  belts 
without  loss,  if  their  weight,  vibratory  motion,  and  tendency 
to  slacken,  did  not  present  obstacles  to  transmission  to  any 
considerable  distance.  Practically,  belts  are  not  generally 
employed  to  transmit  power  to  above  a distance  of  twenty 
or  thirty  feet,  and  more  frequently  the  distance  is  from  ten 
to  fifteen  feet. 


229.  When  power  requires  to  be  carried  to  a distance 
beyond  that  which  belts  can  conveniently  manage,  the 
transmission  is  effected  by  a long  shaft;  and  if  it  be  ne- 
cessary to  change  and  rechange  the  direction  of  the  motion, 
bevel  wheels  are  added.  Or  the  transmission  may  take 
place  by  a long  flat  chain  acting  like  a belt,  but  caused  to 
travel  over  small  wheels  or  pulleys,  to  prevent  the  chain  hang- 
ing down  in  any  part  of  its  course.  A chain  of  this  nature 
is  called  an  endless  chain. 

230.  Motion  is  often  required  to  be  communicated  to 
many  different  machines,  at  different  points,  from  one  source 
of  power.  This  is  effected  by  means  of  a shaft  and  pulleys. 
From  tfie  pulley  which  receives  the  first  motion,  a belt  is 
sent  to  a pulley  fixed  upon  a shaft,  which  shaft  is  generally 
hung  horizontally  from  the  roof  over  the  machines.  As  the 
shaft  turns  through  its  whole  extent,  it  is  able  to  turn  pul- 


SHAFTS  AND  PULLEYS. 


Figure  69. 


B 


leys  fixed  at  any  point  upon 
it,  and  from  these  pulleys, 
belts  are  sent  down  to  pul- 
leys at  the  respective  ma- 
chines. 


A 231.  Figure  69  represents 
an  apparatus  of  a sha  t and 
pulleys.  A is  the  pulley 
receiving  motion  from  the 


190.  What  are  the  disadvantages  of  belts  ? 

191.  How  are  shafts  and  pulleys  used  and  why  ? 

192.  Explain  the  first  diagram. 


78 


CHANGING  VELOCITY. 


source  of  power,  and,  by  means  of  the  belt  L,  turns  the  pulley 
on  the  end  of  the  shaft  S.  At  the  same  time  the  pulley  D at 
the  opposite  end  of  the  shaft  is  turned.  From  a pulley  on 
the  shaft  situated  close  to  B,  a belt  descends  to  turn  C,and 
from  D another  belt  descends  to  turn  E.  Thus,  an  extended 
axle  or  shaft  from  C will  turn  a machine,  and  an  extended 
axle  or  shaft  from  E will  turn  another  machine.  The  ap- 
paratus can  turn  two  machines. 

232.  Shafts  with  pulleys,  working  on  the  plan  now  stated, 
are  to  be  seen  at  almost  every  considerable  manufactory  in 
which  machinery  is  employed;  and  the  power,  by  means 
of  bevel  wheels,  and  upright  connecting  shafis,  is  carried 
upwards  from  story  to  story  in  a building,  giving  motion  to 
hundreds  of  wheels,  spindles  and  other  parts  of  the  mech- 
anism. 


CHANGING  VELOCITY. 

233.  It  is  sometimes  necessary  that  a machine,  or  part 
of  a machine,  should  be  propelled  with  a velocity  which  is 
not  equable,  and  is  continually  changing  from  fast  to  slow 
and  slow  to  fast.  This  happens  in  cotton  mills,  where  it  is 
necessary  that  the  speed  of  certain  parts  of  the  machinery 
should  continually  decrease  from  the  beginning  to  the  end 
of  an  operation.  To  effect  this  an  apparatus  is  used,  as  re- 
presented in  figure  70.  Two  cones,  or 
conically  shaped  drums,  are  used,  hav- 
ing their  larger  diameters  in  contrary 
directions.  They  are  connected  by  a 
belt,  which  is  so  governed  by  proper 
mechanism,  that  it  is  gradually  shifted 
along  from  one  extremity  of  the  cones  to 
the  other,  thus  acting  upon  circles  of  dif- 
ferent diameter,  causing  a continual  change  of  velocity  in 
the  driven  cone  with  relation  to  that  which  drives  it.  1 he 
shifting  of  bands  from  large  to  small  wheels,  and  Iroin 
small  to  large,  has  similar  effects. 


193.  What  examples  of  their  use  are  stated  1 

194.  How  is  velocity  changed  1 


SPRING  AND  CHAIN  APPARATUS. 


79 


PRESERVING  REGULARITY  OF  MOTION  BY  A VARIABLE  FORCE. 

234.  In  some  mechanical  contrivances,  the  force  which 
is  applied  vanes  in  its  intensity,  while  the  wheels  of  the 
machinery  require  to  be  kept  at  a uniform  speed.  This  is 
generally  the  case  when  the  force  is  communicated  from  a 

steel  spring,  which,  after  being 
wound  up,  is  suffered  to  relax. 
Figure  71  is  a spring  suited  for 
operations  of  this  kind.  It  is  re- 
presented in  a state  of  relaxation, 
and  is  wound  up  into  a compact 
form  by  means  of  a spindle  fixed 
to  i'p  inner  extremity.  The  coiling  of  a strip  of  paper  round 
the  finger,  and  allowing  it  to  unwind  itself,  is  a familiar 
illustration  of  the  action  of  a spring  of  this  description. 

235.  The  force  communicated  by  the  relaxing  of  the 
spring  varies  in  its  intensity.  The  force  is  greatest  when 
it  begins  to  relax,  and  it  gradually  weakens  till  its  expan- 
sive energy  is  exhausted.  To  compensate  this  defect,  a very 
ingenious  plan  is  adopted,  and  which  is  put  in  operation 
in  the  apparatus  of  the  common  watch. 

236.  Figure  72  represents  the  apparatus  of  motion  of  a 

watch,  somewhat  magni- 
fied. The  spring  is  con- 
fined in  a brass  cylinder 
or  barrel  B.  To  this 
barrel  the  spring  is  at- 
tached by  a slit  at  its 
outer  extremity.  The 

inner  extremity  of  the  spring  is  fixed  by  a similar  slit  to  the 
central  axis  or  spindle.  F is  a brass  cone,  broad  at  bottom 
and  narrow  at  top,  with  a path  winding  spirally  round  it  as 
an  inclined  plane.  This  cone  is  called  the  fusee,  and  has 
also  a central  axis  or  spindle  K,  to  which  it  is  fixed.  To  a 
point  on  the  lower  inclined  path  of  the  fusee,  a small  steel 
chain  C is  attached,  and  the  other  extremity  of  this  chain 


F,  ;olain  the  first  diagram  and  how  uniform  velocity  is  secured. 


80 


ECCENTRIC  WHEELS. 


is  attached  to  the  top  part  of  the  barrel.  When  the  spring 
is  relaxed,  the  chain  is  almost  altogether  round  the  barrel. 
To  set  the  apparatus  in  motion,  the  watch-key  is  made 
to  turn  the  spindle  K,  by  which  the  chain  is  drawn  from 
the  barrel  to  the  fusee,  filling  up  the  inclined  path  to  the 
summit.  The  chain  in  leaving  the  barrel  causes  it  to  turn, 
and  consequently  to  wind  up  the  spring  inside.  The  pro- 
cess of  unwinding  or  relaxing  ensues,  and  now  the  ingeni- 
ous plan  for  regulating  the  motion  is  to  be  remarked.  At 
first,  when  the  force  of  the  spring  is  greatest,  the  chain 
acts  upon  a small  round  of  the  fusee ; in  other  words,  it 
pulls  with  a small  lever — for  as  already  explained  under  the 
head  Wheel  and  Axle,  a wheel  or  round  object  on  an  axis 
is  simply  a perpetual  lever.  In  proportion  as  the  intensity 
of  the  force  weakens,  and  the  barrel  takes  off  the  chain 
from  the  fusee,  and  winds  it  about  itself,  so  does  the  chain 
act  upon  a longer  lever,  or  so  does  it  gain  a greater  lever 
advantage,  by  drawing  at  a wider  part  of  the  cone.  Thus, 
the  gradual  loss  of  force  is  counterbalanced  by  a gradual 
increase  of  lever  advantage.  (The  case  resembles  that  of 
a strong  man  working  with  a short  lever,  and  a weak  man 
working  with  a long  lever;  both  are  equal  in  effect  in 
balancing  any  resistance.)  The  wheelwork  of  the  watch 
is  moved  by  teeth  on  the  lower  circumference  cf  the  cone. 


ALTERNATE  OR  RECIPROCATING  MOTION — ECCENTRIC  WHEELS. 

237.  Alternate  or  reciprocating  motion  is  applied  to 
movements  which  take  place  continually  backwards  and  for- 
wards in  the  same  path.  In  most  complex  machines,  both 
rotary  and  reciprocating  motion  occur,  and  these  motions 
may  be  converted  into  each  other  by  various  contrivances. 

238.  A common  contrivance  for  gradually  raising  and 
depressing  an  object  by  machinery,  is  that  of  an  eccentric 
wheel. 

239.  An  eccentric  wheel  is  a wheel  with  an  axis  not  in 
its  centre,  but  at  a point  nearer  one  side  than  the  other. 


196.  Explain  the  mechanism  of  a watch. 

197.  How  is  alternate  motion  secured  1 


ECCENTRIC  WHEELS. 


81 


Figure  73.  Figure  73  represents  the  action  of  a wheel 
of  this  kind.  W is  the  wheel,  and  A the 
axis  upon  which  it  is  fixed.  When  the  axis 
turns,  the  wheel  turns  with  it.  As  the  axis 
never  moves  out  of  its  place,  the  wheel  neces- 
sarily describes  a path  of  gradual  rising  and 
falling  in  its  revolutions.  Suppose  an  object,  as  T,  pressing 
upon  the  upper  edge  of  the  w'heel,  so  as  to  accommodate 
itself  to  the  motion,  it  is  obvious  that,  by  the  action  of  the 
wheel,  this  object  will  be  alternately  raised  and  allowed  to 
fall.  Or  suppose  that  a rod  is  hung  from  a point  of  the 
wheel  near  where  T rests,  it  is  similarly  obvious  that  the 
rod  would  be  raised  or  depressed,  according  as  the  wheel 
turned.  Thus,  a rising  and  falling  motion  may  be  effected 
by  an  eccentric  wheel. 

240.  Eccentric  wheels  are  made  of  different  forms.  Ac- 
cording as  they  may  be  required  to  act,  they  are  circular, 
oval,  heart-shaped,  or  pointed  at  one  end,  and  so  forth — the 
i bject  in  each  case  being  to  produce  alternate  motion,  by 
continually  altering  the  distance  of  some  moveable  part  of 
the  machine,  from  the  axis  about  which  they  revolve.  Tech- 
nically, the  projecting  parts  of  eccentric  w'heels  are  called 
cambs. 

241.  In  some  cases,  eccentric  wheels 
are  not  required  to  perform  entire  revo- 
lutions on  their  axes.  It  is  perhaps 
sufficient  for  the  purpose  of  the  me- 
chanism, if  they  gradually  rise  to  the 
height  of  their  power,  and  then,  without 
turning  round,  gradually  descend  by 
retracing  their  course.  An  example 
of  this  kind  of  motion  is  given  in  the 
adjoining  figure.  L is  a lower  circular 
wheel  turning  on  a fixed  central  axle, 
which  axle  rests  on  two  supports  not 
drawn  in  the  figure.  P is  a bar  or  lever 
by  which  the  axle  is  turned.  By  de- 
pressing the  lever  at  P,  the  wheel  turns, 

198.  Explain  the  diagram. 

199.  Name  the  variety  of  eccentric  wheels. 

200.  Explain  the  d agrain. 


Figure  74. 


82 


ECCENTRIC  WHEELS. 


and  by  its  teeth  propels  the  semicircular  eccentric  wheel 
above  it.  The  eccentric  wheel  in  going  forward  is  com- 
pelled to  rise  to  its  full  height,  which  height  it  has  attained 
when  its  extremity  at  F is  brought  straight  above  E.  In 
thus  ascending,  it  pushes  upwards  the  beam  E,  which  is 
attached  to  it  by  an  axle  through  E.  The  beam  E con- 
sequently pushes  up  the  board  M,  and  presses  any  material, 
in  n,  against  the  topmost  board  A B.  This  topmost  boaid 
is  fixed  to  supports,  not  drawn  in  the  figure,  and  neither 
rises  nor  falls.  By  this  process  of  winding  up  the  semi- 
circular eccentric  wheel,  the  utmost  height  of  pressure  of 
the  machine  is  attained.  The  lever  is  then  turned  by  a 
reverse  motion,  and  the  semicircular  eccentric  wheel  conies 
to  its  lowest  depression  when  its  extremity  at  F is  brought 
near  to  L. 

242.  The  principle  upon  which  this  machine  gives  pres- 
sure, is  that  of  the  lever.  In  working. the  lower  circular 
wheel  against  the  eccentric  above,  there  is  a combination 
of  two  levers;  and  the  power  increases  as  the  eccentric 
ascends,  because  the  leverage  of  the  eccentric  is  at  even- 
tooth  increased  in  its  length. 

243.  The  leverage  power  given  by  an  eccentric  wheel  or 
camb  is  one  of  the  most  convenient  and  ingenious  applica- 
tions of  force.  It  is  now  used  in  small  presses  for  stam;>- 
ing  books  and  other  processes  in  which  a^rm  rapid  pres- 
sure requires  to  be  given.  The  example  in  figure  74  is 
that  of  a machine  for  pressing  putty  or  any  other  soft 
material  into  moulds,  to  produce  casts  of  ornaments;  and 
it  appears  to  be  excellently  adapted  for  the  purpose. 

244.  When  an  alternate  rising  and  falling  is  required 
twice  in  a piece  of  machinery,  by  only  one  revolution  of  an 
axle,  an  eccentric  wheel  is  used  of  an  oval  form,  with  the 
axle  in  the  middle  of'the  oval,  by  which  means  each  end 
of  the  oval  rises  in  the  course  of  a revolution. 

245.  When  an  alternate  rising  and  falling  is  required 
thrice,  by  only  one  revolution  of  an  axle,  an  eccentric  wheel 
is  used  having  three  projecting  cambs  on  its  circumference, 
and  as  each  camb  comes  round,  it  lifts  and  lets  fall  any 


201.  Upon  what  principle  is  this  machine  7 


OBLIQUE  ACTION. 


83 


object  presented  to  it.  An  example  of  this  apparatus  is 
Figure  75.  given  in  Figure  75.  The  object 

required  is  to  work  a heavy  ham- 
mer upon  an  anvil  for  beating 
iron.  W is  the  wheel  with  the 
three  cambs,  and  it  turns  by  an 
axle  in  upright  supports.  In  turn- 
ing, each  camb,  with  its  rounded 
or  convex  side,  presses  down  the 
end  of  the  handle  of  the  hammer, 
so  as  to  raise  the  heavy  head  II  at  the  opposite  end.  After 
pressing  down  the  handle  and  escaping,  the  head  of  the 
hammer  falls  with  a heavy  blow  on  the  anvil  A.  There  it 
remains  till  raised  up  and  let  fall  by  the  next  camb,  and 
so  on. 


OBLIQUE  ACTION. 

246.  A mechanical  advantage,  which  is  frequently  of  a 
very  serviceable  nature,  is  obtained  by  causing  the  points 
of  two  straight  bars  to  meet  each  other,  but  fixed  loosely, 
so  as  to  be  free  to  move  from  an  oblique  to  a straight  direc- 
tion, and  the  reverse.  The  power  consists  in  bringing  the 
bars  to  the  straight,  by  which  they  force  asunder  or  press 
hard  upon  any  object  presented  to  their  outer  extremities. 

Figure  76.  In  the  adjoining  figure,  the  bars  are 

l I "w”  seen  first  in  their  oblique  position, 

and  next  when  brought  towards  a 
straight.  Betwixt  the  two  points  a 
small  hollowed  piece  of  metal  is  in- 
serted, in  which  the  points  work,  and 
against  which  the  power  is  exerted 
to  produce  the  action.  The  straight- 
ening and  bending  of  the  apparatus 
resembles  the  action  of  the  knee- 
joint  in  animals.  The  pressure  pro- 
duced by  the  forcing  downwards  of  the  outer  extremity  of 
the  lower  bar  (the  upper  working  against  a fixed  beam)  is 


202.  Explain  the  diagram  and  its  object. 

203.  Whit  of  oblique  action  and  the  example. 


84 


CRANKS  AND  RATCHETS. 


very  easily  and  rapidly  accomplished,  and  is  almost  unlim- 
ited; and  these  advantages,  as  well  as  the  extreme  simpli- 
city of  the  mechanism,  have  led  to  the  application  of  the 
power  to  the  printing-press  wrought  by  the  hand,  instead 
of  screw  pressure. 


CRANKS. 

247.  The  crank  affords  one  of  the  simplest  and  most 
useful  methods  of  changing  an  alternate  rising  and  falling 
motion  into  rotary  motion. 

248.  A crank  resembles  a common  handle  or  winch  for 
turning  a machine  by  the  hand  ; the  chief  difference  being, 
that  a rod  or  shaft  jointed  to  the  handle,  and  going  up  and 
down,  works  the  machine.  If  the  crank  be  made  double, 
it  will  turn  two  wheels  or  machines. 

Figure  77.  249.  Figure  77  represents  a dou- 

ble crank  in  action.  S is  the  rod 
or  shaft  ascending  and  descending, 
and  attached  by  a joint  to  the  lower 
w part  of  the  crank  C,  which  it  alter- 
nately pulls  up  and  pushes  down, 
so  as  to  cause  the  axles  W W to 
turn  a wheel  at  each  side.  Take 
away  one  of  the  sides  of  the  crank 
and  its  support,  and  the  apparatus  becomes  a single  crank. 

250.  Turning-lathes,  knife-grinders’  machines,  and  similar 
apparatus,  are  usually  turned  by  cranks  wrought  by  an 
alternate  pressing  and  raising  of  the  foot  of  the  operator;  a 
rod  going  upwards  from  the  foot-board  to  the  crank,  caus- 
ing the  wheel  or  spindle  to  go  round.  The  crank  has  been 
hitherto  indispensable  in  the  action  of  the  steam  engine. 


RATCHET  WHEELS. 

251.  It  is  sometimes  necessary  to  prevent  wheels  and 
axles,  bearing  the  strain  of  heavy  weights,  from  flying  in  a 
backward  motion  after  being  wound  up.  This  purpose  is 


204.  Define  a crank  and  explain  the  diagram. 
20y.  Cite  examples  of  its  use. 


ACCUMULATING  POWER. 


85 

effected  by  fixing  a ratchet  wheel  to  the  extremity  of  the 
Figure  7S.  axle.  This  wheel  has  teeth  all  round 
its  periphery,  inclining  in  one  direction, 
and  a small  catch  is  so  placed  as  to 
enter  the  indentations  and  stop  the 
wheel  if  it  inclines  to  turn  backwards, 
but  the  catch  slides  over  the  teeth  with- 
out obstructing  them,  if  it  moves  for- 
ward. A spring  pressing  on  the  catch 
causes  it  to  keep  in  its  proper  place.  Figure  78. 

ENGAGING  AND  DISENGAGING  MACHINERY. 

252.  In  many  cases,  particularly  where  numerous  ma- 
chines are  propelled  by  a common  power,  it  is  important 
to  possess  the  means  of  stopping  any  one  of  them  at  plea- 
sure, and  of  restoring  its  motion,  without  interfering  with 
the  rest.  To  produce  this  effect,  various  plans  are  pursued. 
The  most  common  and  simplest  device,  used  in  cases  of 
motion  by  belts,  consists  in  having  a live  and  dead  pulley. 
Alongside  of  the  pulley  whose  axle  moves  the  machinery, 
and  on  which  the  belt  works,  there  is  a pulley  or  wheel 
loose  on  its  axle,  called  the  dead  pulley,  from  its  inopera- 
tive character.  When  the  machine  is  to  be  stopped,  the 
belt  is  shifted  from  the  live  or  active  pulley  to  this  dead 
pulley,  w'hich  it  turns  without  producing  any  effect  on  the 
machinery.  Motion  is  restored  to  the  machine  by  shifting 
the  belt  back  to  the  live  pulley.  A long  rod  with  a clutch 
at  its  extremity,  and  easily  affected  by  the  hand  of  the 
workman,  turns  the  belt  off  or  on  at  a moment’s  notice. 

PRACTICAL  MACHINERY  CONTINUED— OF  AC- 
CUMULATING AND  EQUALISING  POWER. 

ACCUMULATION. 

253.  Power  is  susceptible  of  accumulation — that  is,  of 
increasing  little  by  little — and  of  being  expended  eithei 


206.  What  are  ratchet  wheels  and  their  use. 

207.  How  is  machinery  stopped  at  pleasure. 

208.  What  of  live  and  dead  pulleys  ? 


86 


ACCUMULATING  POWER. 


gradually  or  in  one  or  more  violent  efforts;  the  efforts 
being  entirely  the  concentrated  amount  of  the  previous  ac- 
cumulation. The  apparently  wonderful  powers  displaced 
through  the  agency  of  levers  and  other  simple  machines, 
are  all  a natural  consequence  of  an  accumulation  of  any 
degree  of  force  into  a small  space;  by  which,  effects  take 
place  that  could  never  have  been  accomplished  by  the 
original  force. 

254.  In  consequence  of  this  convenient  accumulation 
of  power  in  machines,  plans  have  been  devised  for  estab- 
lishing reservoirs  of  power,  as  they  may  be  called,  in  con- 
nection with  moving  machinery. 

255.  A well-known  method  of  accumulating  power  con- 
sists in  suspending  a heavy  body  by  a chain  or  strong  rope 
of  considerable  length— forming  what  is  called  by  young 
persons  a swing.  This  body  may  be  put  in  motion  by  a 
very  small  degree  of  power,  and  will  acquire  a vibrating 
motion  like  a pendulum.  By  continuing  the  impulse  as 
the  body  returns,-  it  will  continually  acquire  greater  and 
greater  force,  the  arcs  through  which  it  moves  becoming 
continually  larger,  until  at  last  it  might  be  made  to  over- 
come almost  any  obstacle.  Upon  this  principle,  the  batter- 
ing rams,  or  engines  i or  beating  down  the  fortifications  of 
towns  in  ancient  times,  were  constructed,  and  the  force  of 
their  blows  was  as  great  as  that  of  a cannon  ball ; never- 
theless, the  power  of  their  blows  never  could  exceed  the 
accumulated  power  of  the  impulses  given  to  them  in  order 
to  produce  these  blows. 

256.  The  forcible  expenditure  of  accumulated  power  in 
the  swing  apparatus,  resembles  that  which  is  observable  in 
the  case  of  a person  occupying  several  minutes  in  bending 
a spring — that  is,  accumulating  power — and  then  allowing 
the  spring  to  unbend  itself  by  one  violent  effort,  which 
effort  is  nothing  more  than  the  giving  out  of  the  accumu- 
lated power. 

257.  A boy  taking  a race  to  gain  force  before  making  a 
leap,  is  another  familiar  example  of  accumulating  power 

209.  What  of  reservoirs  of  power  ? 

210.  What  of  battering  rams  ? 

21 1.  What  familiar  examples  are  cited  ? 


ACCUMULATING  POWER.  87 

and  expending  it  instantaneously.  The  boy  is  gathering 
up  power  at  every  step  he  runs,  and  the  force  of  his  kap 
corresponds  exactly  with  the  quantity  of  the  power  he  has 
acquired. 

258.  In  the  same  manner,  the  lifting  of  a hammer,  axe, 
or  other  instrument,  to  an  elevation  as  far  as  our  arm  can 
reach,  in  order  to  give  a blow  with  good  effect,  is  a method 
we  naturally  pursue  to  gain  an  accumulation  of  power. 

259.  In  contrivances  in  the  arts,  power  is  sometimes 
accumulated  in  order  to  be  given  out  in  the  form  of  a rapid 
and  effective  blow.  This  may  be  done  by  nr  ans  of  a 
horizontal  bar  or  lever,  poised  on  a central  axis,  and  loaded 
at  each  end  with  a heavy  ball  of  lead  or  iron.  After  com- 
municating to  the  machine  a sufficient  power  of  rotation, 
it  will  proceed  with  an  enormous  accumulated  energy  and 
momentum,  till  it  expend  its  force  either  by  friction  in 
turning,  or  upon  some  fixed  obstacle  presented  to  it. 

260.  The  press  used  for  stamping  or  taking  impressions 
of  coins  and  similar  articles  from  dies,  furnishes  one  of  the 

Figure  79.  best  examples  of  the  instantaneous  ex- 
L s L penditure  of  accumulated  power.  A 

press  of  this  kind  is  represented  in  figure 
79.  The  apparatusis  very  simple.  It  con- 
sists of  a strong  upright  frame  of  iron, 
with  a thick  screw  S suspended  from  the 
upper  cross  beam,  and  going  through  a 
middle  cross  beam.  In  these  two  beams 
the  screw  works  freely.  The  screw  is 
wrought  by  a horizontal  lever  bar,  poised  on  a central  axis, 
and  loaded  at  each  end  with  a heavy  ball  L L-  The  die 
lies  on  the  point  D below,  and  the  blank  piece  of  metal  to 
be  struck  is  laid  upon  it.  If  a coin  with  two  sides  is  to  be 
impressed,  another  die  is  fixed  upon  the  point  of  the  screw. 
The  rapid  and  forcible  pulling  round  of  the  lever  causes 
the  screw  to  sink,  and  by  a single  rapid  crush  or  blow 
upon  the  metal  against  the  die,  or  dies,  the  impression  is 
made.  The  shock  of  concussion  causes  the  screw  to  re- 
bound upwards,  and  the  instant  a vacancy  is  left  below,  the 


212.  Explain  the  diagram,  and  its  use. 


83  EQUALISING  POWER FLY  VVHEEL3. 

impressed  me'al  is  taken  out,  and  a new  piece  is  inserted. 
By  this  simple  process,  coins,  medals,  ornamented  metal 
buttons,  and  similar  articles,  are  struck. 

EQUALISATION FLY  WHEELS. 

261.  In  most  machines,  both  the  moving  force  and  the 
resistance  to  be  overcome  are  liable  to  fluctuations  of  inten- 
sity at  different  times,  during  the  operation  of  working. 
For  instance,  when  a man  turns  a winch  or  handle  of  a 
piece  of  machinery,  he  is  apt  to  relax  in  his  efforts  for  an 
instant  from  loss  of  strength,  or  from  an  inability  to  keep 
his  attention  closelv  and  uniformly  fixed  to  the  labour  he 
has  to  perforin.  These  relaxations  cause  an  irregularity  of 
motion  in  the  machinery,  which  are  detrimental  to  the 
machine  and  to  the  work  performed.  Other  moving  forces 
are  liable  to  similar  irregularities. 

2ii2.  The  irregularities  in  the  motion  of  machinery,  from 
whatever  cause  they  arise,  are  remedied  by  giving  to  each 
machine  a reservoir  of  power,  from  which  force  may  be 
given  at  all  times  to  equalise  the  motion  according  as  it 
may  be  required.  These  reservoirs  of  power  are  usually  in 
the  form  of  fly  wheels. 

263.  A fly  wheel  is  generally  made 
of  iron,  and  consists  of  a heavy  rim 
or  circumference,  joined  to  a central 
axis  by  cross  bars  or  spokes.  Figure 
80.  In  most  cases  it  is  placed  in 
close  connection  with  the  first  moving 
force,  the  effect  of  which  it  equalises 
in  its  passage  to  the  machine. 

264.  Whatever  quantity  of  power  is 
communicated  to  a fly  wheel,  the  fly 

accumulates  it  and  gives  it  forth  as  may  be  required,  in 
order  to  overcome  any  small  variations  in  the  first  moving 
fijrce  or  in  the  working  of  the  machine. 

265.  The  power  is  communicated  to  the  fly  wheel  at  its 
axle,  and  thence  affects  the  whole  fabric.  The  motion  is 


213.  What  is  the  nature  and  use  of  fly-wheels  1 

214.  Explain  the  diagram. 


OBSTACLES  TO  MOTION. 


89 


a'  first  given  in  a gradual  manner,  till  it  becomes  steady. 
If  there  were  no  machine  to  retard  the  speed,  and  the  im- 
pulsive force  continued  to  be  administered,  the  effects,  from 
centrifugal  force,  would  soon  be  overpowering.  In  prac- 
tice, the  friction  of  the  various  parts  of  the  machine  checks 
the  tendency  to  over  velocity,  and  when  the  machine  lags, 
or  tends  to  work  irregularly,  the  gathered  momentum  of  the 
fly  is  expended  in  preserving  regularity. 

268.  The  weight,  size,  and  velocity  of  fly  wheels,  are 
regulated  bv  the  nature  and  quantity  of  the  power  applied, 
and  the  nature  of  the  machinery  to  be  put  in  motion. 
There  is  a certain  degree  of  velocity  at  which  the  force 
employed  will  produce  the  greatest  effect;  and  it  is  of  im- 
portance to  keep  this  circumstance  in  view,  in  the  construc- 
tion of  machines. 

PRACTICAL  MACHINERY  CONTINUED- 
OBSTACLES  TO  MOTION. 

267.  Moving  bodies,  as  machines  and  wheel  carriages, 
are  less  or  more  retarded  in  their  velocity  by  friction,  and 
the  resistance  of  the  atmosphere,  while  vessels  moving  on 
water  are  retarded  by  the  resistance  both  of  the  atmosphere 
and  of  the  liquid  in  which  they  are  buoyant. 

FRICTION. 

268.  Friction  is  an  effect  of  the  action  of  rubbing  of 
bodies  one  upon  another. 

269.  This  effect  is  produced  by  inequalities  of  surface. 
No  such  thing  is  found  as  perfect  smoothness  of  surface  in 
bodies  In  every  case  there  is,  to  a lesser  or  greater  extent, 
a roughness  or  unevenness  of  the  parts  of  the  surface, 
arising  from  peculiar  texture,  porosity,  and  other  causes; 
and,  therefore,  when  two  surfaces  come  together,  the  promi- 
nent parts  of  the  one  fall  into  the  hollow  parts  of  the  other. 
This  tends  to  prevent  or  retard  motion.  In  dragging  the 

215.  What  particulars  are  important? 

216.  Name  the  various  obstacles  to  motion. 

217.  What  is  the  source  and  influence  of  friction  ? 


DO 


FRICTION. 


one  body  over  the  other,  an  exertion  must  be  used  to  ft 
the  prominences  over  the  parts  which  oppose  them,  and 
this  exertion  is  similar  to  that  of  lifting  or  drawing  of  bodies 
up  inclined  planes  or  over  upright  protuberances.  The 
effect  so  caused  is  called  friction. 

270.  Friction  acts  as  a retarding  influence  in  the  action 
of  all  mechanical  contrivances,  and  a due  allowance  must 
in  every  case  be  made  for  it.  In  many  instances  it  destroys 
more  than  a half  of  the  power  employed,  and  seldom  de- 
stroys less  than  a third.  However  small  it  may  be,  it  sooner 
or  later  causes  the  wearing  down  and  destruction  of  me- 
chanism, and  therefore  forms  an  insurmountable  obstacle  to 
the  lasting  duration  of  bodies  and  the  perpetuity  of  motion. 

271.  The  action  in  overcoming  friction  being  of  the 
nature  of  lifting  or  drawing  of  bodies  up  inclined  planes, 
gravity  is  permitted  to  have  an  effect  in  the  drawing  of 
bodies  upon  horizontal  planes  not  perfectly  smooth.  Thus, 
weight  forms  an  important  element  in  calculating  the  pro- 
bable amount  of  friction  of  a body. 

272.  Friction  is  found  to  depend  on  the  following  circum- 
stances : — 1st,  The  degree  of  roughness  of  the  suriaces.  2d, 
The  weight  of  the  body  to  be  moved.  3d,  The  extent  of 
surfaces  in  certain  bodies  presented  to  the  action  of  rubbing. 
4th,  The  nature  of  the  bodies.  5th,  The  degree  of  velocity 
of  the  motion.  6th,  The  manner  of  (he  motion. 

273.  Roughness. — It  is  of  the  utmost  importance  to 
smooth  the  surfaces.  An  apparently  insignificant  piece  of 
matter,  or  even  particles  of  dust,  will  greatly  retard  the 
motion  of  a body.  But  there  is  a limit  beyond  which  it 
would  be  imprudent  to  smooth  the  surfaces  of  bodies 
having  a close  texture.  If  the  surfaces  be  highly  polished 
and  levelled,  the  bodies  will  adhere  by  the  effect  of  attraction 
of  cohesion,  even  when  the  atmospheric  air  is  not  entirely 
expelled  from  between  them,  and  more  forcibly  when  the 
air  is  completely  expelled.  Practically,  roads,  railways,  and 
similar  bodies,  cannot  be  made  too  smooth. 

274.  Weight. — Friction  from  w'eight  differs  in  different 


218.  What  circumstances  affect  friction  1 

219.  What  of  roughness,  and  weight  1 


FRICTION. 


91 

bodies,  and  depends  on  concurring  circumstances,  as  nature 
of  surface,  and  so  forth.  Friction  always  increases  in  exact 
proportion  as  the  weight  increases,  when  all  other  circum- 
stances remain  the  same.  Any  moving  part  of  machinery, 
therefore,  should  be  made  as  light  as  possible,  consistent 
with  strength  and  durability. 

275.  Extent  of  surfaces. — Rough  bodies  are  more  easily 
drawn  along  when  their  surface  of  contact  is  narrow  than 
w hen  they  are  broad.  For  example,  it  is  easier  to  draw 
two  narrow  brushes  across  each  other,  than  two  broad  ones 
of  the  same  weight.  Friction  may,  therefore,  be  diminished 
in  rough  bodies  by  lessening  the  extent  of  surfaces  in  con- 
tact. But  there  is  a limit  to  this  diminution.  If  the  moving 
surface  be  very  thin,  and  the  other  soft,  the  thin  surface 
w'ill  plough  a groove  in  the  soft  one,  and  thus  the  friction 
w'ill  be  increased,  and  the  machine  injured.  In  the  case 
of  smooth  hard  bodies,  extent  of  surface  makes  no  differ- 
ence in  the  friction. 

270.  Nature  of  Bodies. — It  is  a remarkable  truth  that 
two  bodies  which  are  of  the  same  nature,  or  homogeneous, 
produce  greater  friction  in  movement,  than  bodies  which 
are  different  in  their  nature,  or  heterogeneous.  Thus,  iron 
working  against  iron,  steel  against  steel,  or  brass  against 
brass,  causes  in  each  case  greater  friction  and  wearing  of 
parts,  than  when  iron  or  steel  is  made  to  work  against 
brass.  This  circumstance  is  always  attended  to  in  the 
construction  of  machinery.  Frequently,  a small  piece  of 
leather  is  adjusted  round  an  axle,  to  prevent  the  metals 
from  coming  in  contact. 

277.  Degree  of  Velocity. — Friction  is  a uniformly  retard- 
ing force,  except  in  the  case  of  small  velocities,  when  it  is 
greater  in  proportion.  The  reason  for  it  being  greater  in 
small  velocities,  is,  that  in  these  cases,  time  is  allowed  lor 
the  prominences  of  the  moving  body  to  sink  deeply  into  the 
hollows  of  the  surface  on  which  it  is  moving,  which  has  a 
retarding  effect. 

278.  Manner  of  the  Motion. — The  least  advantageous 


220.  How  is  extent  of  surface  to  be  modified  1 

221.  What  of  the  nature  of  bodies,  and  of  velocity  1 


92 


FRICTION. 


manner  in  winch  one  body  can  be  moved  upon  another,  is 
to  cause  it  to  slide  or  drag.  The  most  advantageous  man- 
ner, is  to  cause  it  to  roll  or  turn.  The  causing  of  a body 
to  roll  instead  of  to  slide,  is  one  of  the  chief  means  of 
diminishing  friction.  The  opposition  presented  bv  inequa- 
lities of  surf-ice  to  a rolling  wheel,  is  overcome  with  ease, 
in  proportion  to  the  extent  of  diameter  of  the  wheel  On  a 
perfectly  horizontal  plane,  the  Irictiou  of  wheels  on  the 
plane  is  very  inconsiderable ; the  chief  seat  of  friction  in 
such  cases,  being  in  the  axles  working  in  their  sockets. 

279.  Various  plans  have  been  tried  to  modify  the  friction 
of  wheels  in  their  sockets.  One  remedy  consists  in  con- 
stantly keeping  up  a lresh  lubrication  from  small  reservoirs 
of  oil  placed  in  the  axles  or  gudgeons,  and  which  supply 
the  deficiency  as  it  occurs.  A more  effectual  plan  consists 
in  surrounding  the  inner  sides  of  the  gudgeons  with  small 
wheels,  upon  the  rims  of  which  wheels  the  axle  works  in 
turning.  These  friction  wheels,  as  they  are  called,  save 
the  axle  from  rubbing  on  the  inner  sur  ace  of  the  gudgeons, 
and  transfer  the  friction  to  their  own  small  axles. 

280.  Friction  is  greatly  diminished  by  lubricating  the 
rubbing  surfaces  with  an  oily  or  greasy  substance,  which 
substance  forms  a medium  of  small  soft  particles  betwixt 
the  bodies,  and  so  prevents  the  tendency  to  grind  or  wear 
down  the  surfaces.  Water  or  any  similar  fluid  will  also  act 
as  a medium  to  prevent  friction,  but  the  effects  are  only  tem- 
porary, and  would  frequently  be  injurious,  as  the  substance 
speedily  evaporates,  and  would  corrode  metals.  Practically, 
fine  pure  oil  is  found  to  be  the  best  unguent  for  machinery. 

281.  One  of  the  first  considerations  on  the  part  of  con- 
trivers of  mechanism,  should  be  how  to  provide  for  and 
diminish  the  effects  of  friction  in  their  machines.  For 
want  of  forethought  on  thi  important  point,  thousands  of 
ingenious  schemes,  which  seemed  perfect  in  the  form  of 
models  and  drawings  on  paper,  have  been  completely 
frustrated  when  attempted  to  be  brought  into  use. 


222.  What  of  rolling  and  sliding  motion  ! 

223.  How  is  friction  modified  in  wheels  ? 


Csr.S  OF  FRICTION. 


93 


USES  OF  FRICTION. 

282.  Whatever  may  be  the  retarding  and  frequently 
inconvenient  effects  of  friction,  in  reference  to  the  action 
of  mechanism,  it  is  certain  that  friction  is  indispensable  in 
the  economy  of  both  nature  and  art,  and  serves  as  an  essen- 
tial auxiliary  to  gravitation.  It  is  a property  which  is 
frequently  necessary,  in  order  to  allow  one  kind  of  matter 
to  possess  a hold  upon  another,  without  actual  cohesion. 
We  walk  and  maintain  our  erect  posture  by  means  of  gravi- 
tation and  action  arid  reaction — in  other  words,  we  are 
held  to  the  earth  by  gravitation,  and  our  pressure  with  our 
feet  exemplifies  action  and  reaction — but  if  there  was  no 
such  property  as  friction,  we  should  either  stick  to  the 
earth  by  attraction  of  cohesion,  or  slide  along  it  as  upon 
the  smoothest  ice.  In  order  to  keep  our  feet  from  sliding 
when  on  ice,  if  we  received  any  impulse,  we  either  tie 
rough  substances  on  our  shoes,  or  scatter  ashes  in  our 
path;  and  thus  we  receive  the  benefit  of  friction.  It  is  by 
friction  that  rains  wear  down  hills,  and  that  rivers  wear 
away  their  banks,  by  which  ceaseless  process  the  external 
configuration  of  the  globe  is  constantly  undergoing  a change. 
The  operations  in  art,  of  washing,  cleaning,  scouring, sharp- 
ening, polishing,  cutting,  bruising,  beating,  and  so  forth, 
are  all  effected  less  or  more  by  friction.  The  hold  which  one 
fibrous  substance  has  on  another,  or  mutual  friction,  permits 
the  operations  of  weaving  cloth,  twisting  ropes  and  threads, 
and  the  tying  of  one  body  to  another.  Thus,  friction  is  of 
universal  service;  and  the  only  known  instances  in  nature 
in  which  it  is  not  required,  and  therefore  not  present,  are 
the  movements  of  the  heavenly  bodies,  which  revolve  in  a 
vacuum,  and  are  consequently  riot  impeded  in  their  motions, 

RESISTANCE  OF  AIR  AND  WATER. 

283.  Atmospheric  air  and  water  are  fluids  of  different 
densities,  and  both  present  an  obstacle  to  the  motion  of 
solid  bodies  through  them. 


225.  Illustrate  the  uses  of  friction. 
228.  What  of  the  heavenly  bodies  ? 


91 


RESISTANCE  OF  AIR  AND  WATER 


284.  There  is  a rule  in  respect  to  the  resistance  pre- 
sented in  moderate  velocities,  which  applies  both  to  air  and 
water.  It  is,  that  the  resistance  is  proportional  to  thf. 
square  of  the  velocity.  For  example,  a velocity  of 
twenty  miles  an  hour  causes  a resistance  four  times  greater 
than  a velocity  of  ten  miles  an  hour,  for  the  square  of 
twenty  (which  is  20  times  20,  or  400)  is  four  times  the 
square  of  ten  (which  is  10  times  19,  or  100).  Thus,  by 
increasing  the  velocity  of  bodies  through  the  air  or  water, 
we  must  increase  the  power  in  a greater  proportion,  in 
order  to  compensate  the  loss  caused  by  resistance. 

285.  Although  the  above  rule  is  nearly  correct  for  mode- 
rate velocities,  it  deviates  considerably  from  what  is  obser- 
vable in  the  case  of  great  velocities,  such  as  that  of  a cannon 
ball.  When  the  velocity  is  upwards  of  1009  feet  per  second 
through  the  air,  the  quick,  passage  of  the  body  is  believed 
to  cause  a partial  vacuum  behind  it,  which  causes  a retarda- 
tion of  its  motion. 

286.  Resistance  to  motion  in  fluids  is  greatly  modified, 
also,  by  the  form  of  the  moving  body.  The  form  that  gives 
least  resistance  is  nearly  that  of  a parabola,  or  a form  some- 
what resembling  the  breast  of  a duck,  the  head  of  a fish^or 
the  rounded  bow  of  a vessel,  sharpened  to  cleave  the  fluid 
through  which  the  body  passes. 

PRACTICAL  MACHINERY  CONCLUDED— MOVING 
FORCES. 

287.  The  sources  of  power  for  moving  machinery  are 
various,  and  are  employed  according  to  circumstances. 
Men  and  animals,  water,  wind,  and  steam,  are  the  principal 
sources,  or,  as  they  are  called,  agents  of  force.  Men  and 
animals  operate  by  muscular  energy;  water  acts  by  its 
momentum  and  gravity;  wind  by  its  pressure  when  in  a 
state  of  motion ; and  steam,  by  the  expansive  energy  of 
heat.  There  are  also  other  agents  of  power  in  nature ; 
such  as  magnetism,  galvanism,  electricity,  and  capillary 

227.  What  is  the  rule  of  resistance  by  air  and  water  ? 

228.  How  with  a cannon  ball  1 

229.  How  does  form  effect  motion  in  fluids  ^ 

230.  Name  the  agents  of  force,  and  their  mode  of  action. 


moving  forces. 


95 


attraction;  but  these  have  hitherto  produced  motion  only 
on  a Jirm  ed  scale. 

HUMAN  LABOUR. 

288.  The  muscular  energy  of  men  forms  the  most  insuf- 
ficient, or  the  weakest,  of  all  the  prime  moving  forces. 
Human  labour  is  very  limited  in  its  compass,  and  is  the 
least  to  be  depended  on  for  regularity.  The  power  exerted 
by  one  man  is  comparatively  small,  and  it  is  both  inconve- 
nient and  expensive  to  cause  a large  number  of  individuals 
to  unite  their  powers  in  a continued  or  concerted  effort. 

289.  The  power  of  a man  to  produce  motion  in  a ma- 
chine, weight,  or  resisting  body,  varies  according  to  the 
mode  in  which  he  applies  his  force,  and  the  number  of 
muscles  which  are  brought  into  action.  In  the  operation 
of  turning  a winch  or  handle  of  a wheel,  as  for  example 
that  of  the  crane,  figure  63,  a man’s  power  changes  in 
every  part  of  the  circle  which  the  handle  describes.  His 
power  is  greatest  when  he  pulls  the  handle  upward  from 
the  height  of  his  knees,  next  greatest  when  he  pushes  it 
down  on  the  opposite  side,  though  here  the  power  cannot 
exceed  the  weight  of  his  body,  and  is  therefore  less  than 
can  be  exerted  in  pulling  upward.  His  power  is  weakest 
when  at  the  top  and  bottom  of  the  circle,  where  the  handle 
is  pushed  or  drawn  almost  horizontally. 

290.  A man  can  exert  the  greatest  active  strength  when 
he  is  at  rest  in  his  person  (that  is,  not  walking),  and  when 
he  pulls  or  lifts  a body  upwards  from  his  feet,  because  the 
strong  muscles  of  his  back,  as  well  as  those  of  his  arms 
and  legs,  are  then  brought  advantageously  into  action,  and 
the  bones  are  favourably  situated,  by  the  fulcra  of  the  levers 
being  near  to  the  resistance.  Hence,  the  action  of  rowing, 
or  pulling  oars,  is  one  of  the  most  advantageous  modes  of 
muscular  exertion.  In  that  operation,  the  whole  frame 
exerts  itself  in  the  most  favourable  manner ; and  no  method 
which  has  been  devised  for  propelling  boats  by  the  labour 
of  men,  has  hitherto  superseded  it. 

231.  What  of  muscular  power  7 

232.  How  does  this  vary  as  in  turning  a crank  7 

233.  How  may  the  greatest  strength  be  exerted  7 


HUMAN  LABOUR. 


9f> 

291.  It  is  usual,  in  estimating  the  amount  of  power  which 
can  be  exerted  by  animals,  to  reckon  it  by  the  weight 
which  the  animal  can  lift  in  a given  length  of  time  to  a 
given  height.  By  this  standard,  it  is  computed  that  a man 
of  ordinary  strength  ran  raise  a weight  of  10  pounds  to  the 
height  of  10  feet  once  in  a second,  and  continue  this  labour 
for  10  hours  in  the  day.  This  is  supposing  him  to  use  his 
force  under  common  mechanical  advantages,  and  without 
any  deduction  from  friction. 

292.  All  such  estimates  as  this,  however,  are  exceedingly 
illusive.  The  ability  for  exercising  power  varies  in  different 
countries,  and  depends  greatly  on  exercise  and  diet.  There- 
fore, no  practically  useful  calculations  can  be  made  regard- 
ing it. 

293.  Human  strength,  as  has  been  said,  can  be  exerted 
with  greatest  effect  in  lifting  from  the  ground,  and  pulling 
as  with  an  oar.  But  this  species  of  action  produces  ex- 
haustion; and  hence  the  advantage  is  neutralized  by  a 
certain  disadvantage.  The  way  in  which  the  greatest  effect 
can  be  produced  by  human  labour,  with  a moderate  degree 
of  fatigue,  is  simply  to  allow  the  weight  or  gravity  of  the 
person  to  work.  For  example,  let  a man  walk  up  a ladder 
to  a certain  height,  and  then  stepping  into  a bucket  which 
is  attached  to  a cord  and  pulley,  permit  himself  to  sink 
with  the  bucket  to  the  ground,  drawing  up  a load  at  the 
other  end  of  the  cord.  Whatever  be  his  weight,  he  will 
be  able  to  raise  at  each  descent  a load  nearly  as  great;  and 
therefore,  by  such  a plan,  would,  in  the  course  of  a day, 
raise  a great  deal  more  weight  of  material  to  the  top  of  a 
house,  than  by  the  common  process  of  carrying  up  a mass 
of  matter  in  his  hands  or  on  his  shoulders. 

294.  In  giving  effect  to  the  gravity  of  the  person,  no 
exertion  is  used  ; and  the  only  source  of  fatigue  is  that  of 
walking  up  an  inclined  plane  to  obtain  a due  elevation. 
According  to  the  principle  defined  in  paragraph  135,  the 
expenditure  of  exertion  in  ascending  inclined  planes,  is  not 
according  to  the  degree  of  inclination,  but  according  to  the 


234.  What  estimate  has  been  made  of  animal  power  t 

235.  What  illustrations  are  cited  7 


HUMAN  LABOUR. 


97 


elevation  reached;  this  is  agreeable  to  the  rule  of  mecha- 
nics mentioned  in  paragraph  17,  namely,  that  a small  force 
exerted  for  a long  period  of  time  is  equivalent  to  a great 
force  exerted  lor  a short  period  of  time.  Thus,  nearly  the 
same  degree  of  animal  fatigue  is  incurred  by  reaching  the 
same  elevation  in  the  same  time,  whatever  be  the  ineliu a- 
tion  of  the  ascent. 

295.  In  walking  on  a perfectly  horizontal  plane,  the 
gravity  of  the  person,  in  ordinary  cases,  is  not  felt;  for  the 
fabric  of  the  body  is  so  nicely  balanced,  and  the  weight  so 
generally  borne  by  the  different  parts  that  we  are  hardly 
conscious  of  the  exertion.  When  we  try  to  ascend  a hill, 
we  begin  to  feel  that  our  gravity  retards,  and  consequently 
fatigues  us,  for  we  are  pulling  against  the  force  of  terres- 
trial attraction.  But  when  we  commence  descending  a hill, 
we  feel  that  we  are  greatly  assisted  by  our  gravity — that  is, 
we  are  allowing  attraction  to  pull  us.  We  are  also  assisted 
in  descending,  by  an  acquired  momentum  in  our  person. 

Figure  81.  29b.  The  mo- 

ving power  given 
to  machinery  by 
the  mere  gravity 
of  the  person,  is 
seldom  used  ex- 
cept in  the  case 
of  involuntary  la- 
bour at  the  tread- 
mill. A tread-rnill 
is  a large  broad  wheel  with  steps  all  round  on  its  circumfer- 
ence, and  on  which  steps  men  are  compelled  to  ascend,  hold- 
ing on  by  a fixed  bar  or  rail  in  front.  The  weight  of  the 
men  turns  the  wheel,  which,  by  turning  an  axle,  gives  mo 
tion,  if  necessary,  to  certain  machinery.  The  tread-mill 
thus  forms  a revolving  or  endless  stair.  Figure  81  repre- 
sents one  of  these  machines  in  operation.  A is  the  axle, 
S are  the  steps,  and  P is  a fixed  platform  in  front  of  them. 

297.  It  is  evidently  disadvantageous  to  employ  human 


236.  What  of  ascending  and  descending  a hill  ? 

237.  Explain  the  tread  mill. 


98 


HORSES  POWER DRAUGHT. 


labour  as  a moving  power,  except  in  cases  in  which  the 
force  required  is  so  small  as  not  to  require  further  aid,  or 
where  skill  as  well  as  muscular  energy  is  necessary.  The 
human  being  has  been  designed  for  executing  higher 
duties  than  those  which  can  be  adequately  performed  by 
the  lower  animals,  and  by  the  agency  of  inanimate  forces. 

298.  The  power 
of  the  ass  is  some- 
times employed  as 
a moving  force,  in 
operations  not  re- 
quiring great  la- 
bour, and  on  a 
principle  similar  to 
that  of  the  tread- 
mill. At  Caris- 
brook  Castle,  in 
the  Isle  of  Wight, 
an  ass  was  lately 
employed  to  move  a machine  acting  like  a windlass  for 
drawing  water  from  an  exceedingly  deep  well.  The  animal 
acted  entirely  by  giving  effect  to  its  weight,  as  represented 
in  figure  82 

horse’s  POWER DRAUGHT. 

299.  Horses  and  oxen  are  used,  in  all  countries  where 
they  exist,  as  agents  of  force.  Horses  are  more  valuable 
for  this  purpose  than  oxen,  because  they  are  generally  more 
tractable,  and  otherwise  better  suited  for  the  labour.  Oxen 
are  used  only  for  draught. 

300  A horse  employs  two  forces  in  drawing — the  force 
of  his  muscular  energy  exerted  against  the  resistance  of  his 
hind  legs  and  feet,  and  the  force  of  his  weight  or  gravity. 
Power  of  draught  is  estimated  according  to  the  constitu- 
tional strength,  height  of  breast  from  the  hind  feet,  and 
weight  of  the  animal. 

301.  The  force  of  a horse  diminishes  as  his  speed 


233".  What  does  the  last  diagram  show  ? 

239.  VVliat  of  oxen  and  horses  and  their  forces  ? 


horse’s  POWER  — DRAUGHT. 


99 


increases  beyond  a certain  limit.  If  the  load  that  he  can 
pull,  when  moving  at  the  rate  of  two  miles  in  an  hour,  is 
represented  by  109,  that  at  three  miles  in  an  hour  will  be 
81 — at  f>ur  miles  in  an  hour,  G4 — at  five  miles  in  an  hour, 
49 — and  at  six  miles  in  an  hour,  36.*  In  this  way  the 
draught  of  a horse  continues  to  diminish,  till  he  attains  his 
greatest  speed,  when  he  can  barely  carry  his  own  weight. 

302.  A horse  exerts  his  power  most  advantageously,  when 
walking  at  the  rate  of  about  four  miles  in  an  hour.  This 
advantageous  rate  of  speed,  however,  does  not  apply  in  the 
case  of  short  efforts.  In  these,  a rapid  motion,  to  get  at 
once  over  the  difficulty,  is  most  advantageous  for  the  mus- 
cular energy. 

303.  There  are  various  estimates  of  a horse’s  power,  but 
that  of  James  Watt  is  generally  adopted  as  the  standard. 
The  measure  of  a horse’s  power,  according  to  Mr.  Watt,  is, 
that  he  can  raise  a weight  of  33,090  pounds  (for  instance, 
drawing  it  over  a pulley)  to  a height  of  one  foot  in  a minute. 

394.  In  comparing  the  strength  of  horses  with  that  of 
men,  it  is  estimated  that  the  force  of  one  horse  is  equal  to 
that  of  five  men.  But  this  estimate  is  liable  to  certain  im- 
portant exceptions.  Much  depends  on  the  manner  in  which 
the  exertion  takes  place. 

305.  Any  body  moving  forward  on  a smooth  horizontal 
plane,  can  be  drawn  with  the  least  possible  force,  when  the 
line  of  draught  is  straight  in  a horizontal  line  from  the  power 
to  the  point  of  resistance.  But  a horse,  in  drawing,  can  use  his 
weight  and  muscular  energy  with  greatest  advantage  when 
the  line  of  draught  inclines  from  the  load  upward  to  his 
breast.  Thus,  the  convenience  of  the  horse  must  always 
be  consulted  in  practical  operations. 

396.  A horse,  also,  can  pull  a wheeled  carriage  with 
greater  advantage  when  the  wheels  are  large  than  when 
they  are  small,  because  large  wheels  get  most  easily  over 

* These  proportions  are  given  by  Professor  Leslie,  and  are  confirmed 
by  the  observations  of  other  experimental  mechanics. 


240.  How  is  the  force  of  a horse  calculated  ? 

241.  Mr.  Watt’s  estimate. 

242.  How  does  it  compare  with  the  power  of  man  1 

243.  How  should  the  line  of  draught  be  regulated  ? 


100 


horse’s  POWER DRAUGHT. 


Figure  83. 


obstacles  lying  before  them.  This  is  an  evident  truth,  but 
it  can  be  proved  by  an  appeal  to  the  principle  of  the  lever. 

307.  The  operation  of  drawing  a wheeled  vehicle,  pre- 
sents an  example  of  lever  action  of  a peculiar  kind.  The 
load  of  the  vehicle,  or  the  weight , presses  on  the  nave  or 
axle  of  the  wheel,  and  the  direction  of  its  action  thence 
passes  down  in  a straight  line  to  the  plane  on  which  the 
vehicle  rests.  The  direction  of  the  power  is  a line  from 
the  moving  agent  to  the  axle.  If  the  plane  be  perfectly 
smooth,  the  fulcrum  is  identified  with  the  point  on  which 
the  weight  presses  on  the  ground.  If  any  obstacle  be 
placed  before  the  wheel,  then,  that  obstacle,  at  the  instant 
of  contact,  becomes  the  fulcrum 

308.  Figure  83  represents  a wheel,  with  an  obstacle, 
which  we  may  suppose  to  be  a 
stone,  lying  before  it.  The  line 
of  draught  P A is  the  direction 
of  the  power.  A horse  may  be 

■P  supposed  to  be  pulling  at  P.  The 
line  A W is  the  direction  of  the 
weight.  F is  the  obstacle,  or 
fulcrum,  upon  which  the  power 
has  to  act.  A line  from  A to  F may  represent  the  lever, 
having  the  fulcrum  F at  one  extremity,  and  the  power  and 
weight  applied  to  the  other  extremity  A.  The  apparatus 
is  thus  a lever  of  oblique  action  with  a single  arm.  Accord- 
ing to  the  rules  laid  down  for  estimating  the  power  of  bent 
levers,  the  arm  of  power  is  an  ideal  line  drawn  at  right 
angles  from  the  line  A P to  F,  and  the  arm  of  weight  an 
ideal  line  drawn  at  right  angles  from  the  line  A W to  F. 
The  mechanical  advantage  is  calculated  from  these  two 
ideal  lines.  By  increasing  the  diameter  of  the  wheel, 
these  ideal  lines  increase,  but  that  of  the  power  increases 
in  the  greatest  proportion,  and  hence  the  advantage  of 
increasing  the  diameter  of  wheels. 

309.  It  is  customary  to  place  small  wheels  before  large 
ones  in  four-wheeled  carriages.  This  is  done  only  for 
the  sake  of  convenience  in  turning  the  vehicle  ; if  the  front 


244.  What  of  wheels  and  their  motion  J 

245.  Explain  the  diagram. 


HORSu’s  POWER DRAUGHT. 


JOi 


wheels  were  made  as  large  as  the  hind  ones,  the  carriage 
would  be  more  easily  drawn. 

310.  In  yoking  several  horses,  one  before  the  other,  to 
ploughs  or  wheeled  carnages,  it  is  of  importance  to  cause 
the  line  of  draught  of  all  the  horses  to  proceed  in  a straight 
linetothepointof  resistance,  or  as  nearly  so  as  is  convenient. 
The  resistance  of  the  plough  is  in  the  sock  or  cutting  part 
in  the  earth,  and  the  resistance  of  the  load  in  wheeled  car- 
riages, is  at  the  axles.  The  distance  of  the  animals  from 
the  machine  they  are  drawing,  is  of  little  consequence, 
provided  each  horse  is  able  to  exert  his  force  directly  in  a 
line  to  the  resistance. 

311.  Horses  draw  with  best  effect  when  they  aie  yoked 
singly  or  abreast.  In  yoking  them  one  before  the  other,  a 
portion  of  their  force  is  generally  expended  uselessly,  if  not 
mischievously,  in  hampering  each  other.  When  a horse 
draws  a four-wheeled  carriage,  the  line  of  his  draught  should 
go  to  a point  between  the  two  axles,  and  come  over  the 
front  axle.  The  same  rule  holds  with  two  or  more  horses 
in  four-wheeled  vehicles. 

312.  Wheels  have  least  friction  where  they  are  narrow  in 
the  rim,  but  this  is  supposing  the  road  to  be  hard  and 
smooth.  In  cases  of  great  weights,  and  when  the  roads  are 
not  very  smooth  or  hard,  broad  wheels  are  the  best  for  both 
safety  and  draught.  Wheels  which  are  perfectly  straight 
or  upright  are  pulled  with  less  exertion  than  wheels  which 
are  of  a dished  form — that  is,  with  the  spokes  sloping  to 
the  rim  ; but  the  dished  form  is  of  use  in  widening  the 
base  and  preventing  overturning;  it  is  also  particularly 
useful  where  the  road  is  inclined  to  one  side,  as  the  spokes 
of  the  lower  wheel,  which  then  support  more  than  half  the 
weight,  are  more  nearly  in  a vertical  direction,  and  there- 
fore resist  the  pressure  with  the  greatest  effect ; so  that 
when  the  load  is  thus  increased  upon  them,  their  resisting 
power  is  at  the  same  time  increased. 

313.  When  the  load  is  suspended  on  springs,  the  shocks 

246.  Why  the  difference  in  the  wheels  of  carriages  ? 

247.  What  of  the  point  of  resistance  in  draught  ? 

248.  What  of  more  horses  than  one  1 

249.  What  of  a variety  in  wheels  t 


102 


DRAUGHT  OF  WHEELED  CARRIAGES: 


caused  by  friction  in  movement  are  lessened — that  is,  the 
force  of  the  concussions  is  spent  upon  the  elasticity  of  the 
spring,  a circumstance  of  great  convenience  to  passengers 
in  carriages.  The  elasticity,  also,  preserves  equability  of 
weight  to  the  horse.  At  every  jolt  over  a protuberance, 
without  springs,  the  load  receives  a momentum  in  descend- 
ing, which  on  being  checked  gives  a shock  to  the  animal 
in  the  shafts;  whereas,  in  using  springs,  the  weight  has 
always  a comparatively  equal  pressure. 

314.  Horses  communicate  moving  power  to  machinery, 
by  being  yoked  to  a horizontally  turning  beam  or  wheel, 
and  walking  in  a circle.  The  motion  of  the  beam  or  wheel, 
by  acting  on  a pinion  and  shaft,  moves  the  machinery.  Many 
mills  are  turned  in  this  manner.  To  give  full  advantage  to 
the  capacity  of  the  horse,  the  circle  should  not  be  less  than 
from  thirty  to  forty  feet  in  diameter. 

Figure  84. 


315.  Figure  84  represents  the  action  of  horse  power  upon 
a mill.  U is  an  upright  axle  working  on  pivots,  from  which 
axle  a beam  B B is  projected,  and  into  which  two  horses 
H H are  yoked.  W is  a horizontally  moving  wheel  on  the 
axle,  which  wheel  turns  a trundle  T fixed  to  the  shaft  S. 
The  turning  of  the  shaft  moves  the  machinery. 

316.  The  same  principle  applies  with  respect  to  the  em- 
ployment of  horses  and  other  animals,  as  agents  of  force,  as 


250.  Of  what  advantage  are  springs  ? 

251.  How  do  horses  best  move  in  machinery  7 

252.  Explain  the  diagram. 


WATER  POWER. 


103 


that  which  applies  to  human  labour  (paragraph  297.)  An 
animal  is  only  employed  advantageously  when  he  is  caused 
to  do  work  which  could  not  be  as  conveniently  executed 
by  inanimate  forces.  In  all  cases  in  which  inanimate  forces 
can  be  conveniently  substituted  for  animal  power,  the  ap- 
plication of  the  animal  is  not  legitimate,  because  only  its 
weight  and  muscular  energy  are  brought  into  operation, 
and  its  sagacity,  which  is  frequently  a valuable  part  of  it, 
lies  unemployed. 

WATER  POWER. 

317.  Water  acts  as  a first  mover  by  the  force  of  its  gravity 
or  weight ; and  also  in  some  cases  by  its  momentum  or  im- 
pulsive power  It  is  applied  by  causing  it  to  fall  or  flow 
upon  the  outer  part  of  a wheel,  which  turns  with  the  force. 

318.  Water  power,  if  to  be  had  in  a sufficient  quantity, 
is  preferred  to  all  other  powers,  in  consequence  of  its  sim- 
plicity of  action,  extraordinary  cheapness,  and  steadiness. 

319.  The  mode  of  applying  water  power  to  a wheel  de- 
pends on  the  extent  of  the  fall,  or  the  height  of  the  stream 
at  the  point  where  it  can  be  properly  applied.  It  is  of 
importance  to  have  as  great  an  extent  of  fall  as  possible  ; 
but  at  the  same  time,  a certain  declivity  must  be  left  below 
the  mill,  in  order  to  allow  the  wrater  to  flow  freely  away, 
and  not  obstruct  the  wrheel  in  its  motion. 

320.  Two  chief  kinds  of  water-wheels  are  used  according 
to  the  extent  of  the  fall,  and  the  nature  of  the  stream. 
When  the  water  cannot  be  made  to  approach  the  wheel, 
higher  than  a point  opposite  the  middle  of  the  wheel,  a 
breast  wheel  is  used.  The  w ater  is  brought  by  an  artificial 
channel  and  permitted  to  flow  or  fall  into  buckets  fixed  in 
the  outer  circumference  of  the  wheel.  The  weight  of  the 
w'ater  in  the  buckets,  presses  down  the  wheel  and  causes  it 
to  turn.  When  the  buckets  come  to  the  bottom  in  revolving, 
they  let  the  water  flow  from  them,  and  go  up  empty  on  the 
other  side,  ready  to  be  again  filled. 

253.  What  is  said  of  animal  agency  in  machinery  ? 

254.  What  of  water  power  and  its  advantages  ? 

255.  How  is  it  best  applied  ? 

256.  Describe  both  kinds  of  water-wheels. 


104 


WATER  POWER. 


321.  Figure  85  represents  the  action  of  a breast  water- 


koned  the  height  of  the  fall.  The  axle  of  the  wheel  in  this 
case  turns  the  machinery  ; but  sometimes  the  wheel  has 
teeth  round  its  circumference,  which,  working  on  a pinion, 
turns  the  machinery. 

322.  When  the  fall  is  considerable,  or  when  the  water  can 
be  made  to  approach  by  a channel  on  a level  with  the  top  of 
the  wheel,  an  overshot  wheel  is  used.  The  water  is  allowed 
to  fall  into  the  buckets  at  the  top,  so  as  to  act  much 
more  advantageously  than  if  it  fell  at  a lower  level.  It  is 
seldom  that  streams  can  be  conveniently  brought  to  operate 
in  this  advantageous  manner. 

323.  Water  power,  acting  either  by  breast  or  overshot 
wheels,  is  a much  more  effective  and  steady  agent  of  mov- 
ing force  than  wind.  Windmills  are  used  only  in  cases  in 
which  perfect  regularity  and  constancy  of  motion  are  not  re- 
quired, and  where  water  cannot  be  obtained  at  a sufficient 
height  to  form  a fall. 

STEAM  POWER. 

324.  Water  boils  at  212  degrees  of  Fahrenheit’s  ther- 
mometer, under  the  common  atmospheric  pressure;  and  the 
application  of  fire,  after  it  reaches  the  boiling  point,  causes 
it  to  fl  v off  in  the  form  of  vapour  or  steam.* 

325.  A cubic  inch  of  water  produces  almost  exactly  a 
cubic  foot  of  steam,  or  1728  cubic  inches.  In  its  expan- 
sion therefore  it  exerts  enormous  force,  and  this  circum- 
stance has  rendered  it  valuable  as  a source  of  pow'er. 

* See  Laws  of  Matter  and  Motion,  in  which  the  subject  of  heat 
in  application  to  water  is  fully  treated  of. 


Figure  85. 


wheel.  W is  the  water 
flowing  from  a channel  L 
into  the  buckets  B B, 
which  are  supposed  to  be 
seen  through  the  sides  of 
the  rim ; these  buckets 
are  emptied  on  coming 
down  to  F,  and  the  water 
flow's  aw'ay  in  the  channel 
C.  F rom  W,  to  F is  rec- 


257.  Explain  the  diagram. 

258.  What  of  wind  as  au  agent  of  force  ? 


STEAM  POWER. 


105 


326.  Steam  is  applied  to  machinery  by  means  of  a boiler 
and  an  apparatus  called  the  steam-engine.  Steam-engines 
are  of  different  constructions,  and  improvements  and  simpli- 
fications are  continually  taking  place  in  their  character  and 
mode  of  working.  The  power  exerted  by  steam-engines, 
is  estimated  according  to  the  horse  powers  to  which  they 
are  equal,  and  which  there  are  certain  rules  for  calculating. 

327.  There  are  two  distinct  kinds  of  engines,  namely, 
high-pressure  or  non-condensing,  and  low-pressure  or  con- 
densing. The  high-pressure  engine  is  the  most  simple 
in  its  construction.  The  steam,  generated  in  a boiler, 
rushes  through  a tube  to  the  cylinder,  which  is  a close 
round  vessel  like  a barrel.  It  enters  the  cylinder  at  two 
openings,  one  at  the  bottom  and  the  other  at  the  top. 
The  steam  which  enters  at  the  lower  opening  drives  up  a 
round  object  or  plug,  fitting  nicely  to  the  cylinder,  and 
called  the  piston,  to  the  top,  whence  it  is  driven  down 
again  to  the  bottom  by  the  steam  which  enters  at  the 
upper  opening  ; the  steam  used  in  both  cases  being  with- 
drawn to  allow  the  action.  An  external  rod  from  the  pis- 
ton, thus  driven  up  and  down,  passes  out  of  the  cylinder 
at  a small  orifice  at  the  top,  and  affects  the  beam,  which, 
turning  a crank,  moves  the  machinery.  In  this  kind  of 
engine,  the  steam,  on  performing  its  office  of  depressing  and 
raising  the  piston,  is  allowed  to  escape  into  the  atmosphere; 
and  the  engine  is  called  high-pressure,  because,  steam  of  a 
high  degree  of  pressure  has  to  be  employed  to  counteract 
the  pressure  of  the  atmosphere  on  the  escaping  steam. 

328.  The  low-pressure  or  condensing  engine  is  supplied 
with  steam  in  much  the  same  manner,  but  the  mode  of 
withdrawing  and  destroying  the  used  steam  from  the  cylin- 
der is  totally  different,  As  soon  as  the  steam,  which  rushes 
in  at  the  lower  opening  of  the  cylinder,  has  driven  the  pis- 
ton upwards,  it  is  instantaneously  abstracted  or  withdrawn 
into  a separate  vessel  below,  called  the  condenser,  where  it. 
is  condensed  by  a squirt  of  cold  water,  and  runs  off  into  a 
cistern  ; from  which  cistern  the  water  in  a warm  state  is 


259.  What  is  said  of  steam  ? 

260.  What  principle  of  steam  is  the  source  of  power  7 

261.  By  whnt  means  is  it  applied,  and  how  calculated  7 

262.  Describe  a high-preseure  engine,  and  why  so  named  ? 


106 


STEAM  POWER. 


pumped  into  the  boiler  to  make  new  steam.  The  same 
process  takes  place  with  the  steam  which  drives  the  piston 
downwards.  The  abstraction  of  the  steam  into  the  con- 
denser is  effected  by  an  air-pump  (wrought  by  the  engine), 
which,  at  the  proper  instant  of  time,  pumps  out  the  water 
produced  by  the  condensed  steam,  and  that  of  the  condens- 
ing jet,  and  also  any  air  that  may  collect,  and  forms  a par- 
tial vacuum  in  the  condenser.  As  this  vacuum  presents 
no  obstacle  to  the  action  of  the  piston,  in  other  words,  as 
the  steam  is  not  opposed  by  the  atmosphere  in  making  its 
escape  from  the  cylinder,  the  steam  requires  to  be  of  com- 
paratively small  force — much  smaller  than  if  the  pressure 
of  the  atmosphere  had  to  be  overcome  ; it  is  therefore  called 
a low-pressure  engine. 

329.  The  low-pressure  or  condensing  engine,  just  no- 
ticed, is  also  called  a double-acting  engine,  because  Us 
piston  is  driven  both  up  and  down  by  steam.  There  are 
low-pressure  engines  called  single-acting  engines.  These 
have  the  piston  acted  upon  by  steam  only  in  the  down 
stroke,  the  up  stroke  or  return  of  the  piston,  being  pro- 
duced by  the  action  of  a counterweight  on  the  farther 
extremity  of  the  beam. 

330.  Figure  86  represents  a rudimental  outline  of  the 

Figure  86. 


STEAM  POWER. 


107 


action  of  steam  power,  whether  in  high  or  low-pressure  en- 
gines. A is  the  pipe  by  which  the  steam  is  conducted 
from  the  boiler  to  the  cylinder  E E,  by  means  of  the  pipe 
B into  the  cylinder  E E at  the  upper  opening  C and  the 
lower  opening  D.  F is  the  piston  with  a rod  G going  up  to 
the  end  of  the  beam  H.  This  beam  moves  up  and  down 
on  a central  axis  I.  From  the  extremity  of  the  beam  at  L, 
a shaft  M goes  down  to  the  crank  on  the  pulley  N,  which 
it  turns.  From  N a belt  O is  carried  to  the  pulley  R,  and 
a shaft  from  this  pulley  moves  the  machinery.  S is  a fly 
wheel  working  close  beside  the  crank  pulley.  The  pipe  T 
is  the  path  for  the  escape  of  the  steam  from  the  cylinder 
after  performing  its  office.  At  the  different  openings  in  the 
communication  pipes,  there  are  little  doors  or  valves,  which 
are  opened  and  shut  as  is  required  to  admit  or  allow  the 
escape  of  the  steam  ; but  these  valves,  and  also  many  minor 
parts  of  the  mechanism,  are  for  the  sake  of  clearness  not 
marked  in  the  figure,  and  the  steam  engine  should  be  seen  in 
actual  operation,  if  a perfect  idea  of  the  apparatus  is  desired. 

33 L.  Steam  power,  when  properly  organized,  possesses 
the  quality  of  great  steadiness  of  action,  in  which  it  almost 
equals  water  power.  It  is  therefore  adapted  for  turning  all 
kinds  of  machinery,  and  may  be  employed  in  every  imagi- 
nable situation  where  fuel  and  water  exist.  The  most  won- 
derful of  its  achievements  is  the  propulsion  of  vessels  at 
sea,  and  vehicles  on  railways  upon  land. 

332.  The  steam  power  at  present  employed  in  Great 
Britain  and  Ireland,  is  equal  to  about  8,000,000  of  men's 
power,  or  1,600,0110  horse  power.  It  is  calculated  that  a 
horse  requires  eight  times  the  quantity  of  soil  for  producing 
food  that  a human  being  does  ; if,  therefore,  horse  power 
were  made  to  supersede  steam  power,  additional  food  for 
1,600,000  horses  would  require  to  be  raised,  which  would 
be  equal  to  the  food  of  12,800,000  men.  [As  the  amount 
of  steam  power  employed  in  America  is  more  than  ten  times 
that  in  Great  Britain  and  Ireland,  these  calculations  must  all 
be  increased  tenfold,  if  we  would  approximate  the  import- 
ance  of  this  agent  in  our  country.] 

333.  It  is  in  consequence  of  the  improved  mechanical 


266.  To  what  useful  purposes  is  steam  applied  ? 

267.  What  calculations  are  made  ? 


108 


STEAM  POWER. 


arrangements,  and  employment  of  inanimate  forces  in  Great 
Britain,  that  that  comparatively  small  country  is  enabled 
to  manufacture  goods  cheaper,  and  with  greater  profit,  than 
can  be  done  by  the  largest  and  most  populous  countries 
in  which  mechanism  is  imperfect,  and  labour  performed 
exclusively  by  living  agents. 

334.  The  profits  of  manufacture  so  produced,  spread 
their  beneficial  influence  over  the  whole  mass  of  society, 
every  one  being  less  or  more  benefited.  Thus,  almost  all 
the  luxuries  and  comforts  of  life,  all  the  refinements  of  social 
existence,  may  be  traced  to  the  use  of  tools  and  machinery. 
Machinery  is  the  result  of  mechanical  skill,  and  mechanical 
skill  is  the  result  of  experience  and  a long  course  of  inves- 
tigation into  the  working  of  principles  in  Nature,  which 
are  hidden  from  the  inattentive  observer.  Much  of  the 
present  mechanical  improvement  is  also  owing  to  the  pres- 
sure of  necessities,  or  wants,  which  have  always  a tendency 
to  stimulate  the  dormant  powers  of  man.  What  are  to 
be  the  ultimate  limits  and  advantages  of  mechanical  dis- 
coveries, no  one  can  foresee.  The  investigation  of  natural 
forces  is  yet  far  from  being  finished.  Every  day  discloses 
some  new  scientific  truth,  which  is  forthw  ith  impressed  into 
the  service  of  mankind,  and  tends  to  diminish  the  sum  of 
human  drudgery  and  suffering.  In  this  manner,  therefore, 
are  we  usefully  taught,  that  the  study  of  .Nature  forms  a 
never-failing  source  of  intellectual  enjoyment,  and  that 
“ Knowledge  is  Power.” 

The  subject  of  the  next  Treatise  is  Hydrostatics,  or 
the  Laws  of  Fluids. 


26S.  Name  some  of  the  advantages  derived  from  it. 

269.  Are  not  still  further  improvements  probable  ? 

270.  To  what  source  are  we  to  look  for  their  discovery  1 


THE  END. 


ELEM  ENTS 


OF 

NATURAL  PHILOSOPHY. 


PART  III. 

HYDROSTATICS,  HYDRAULICS, 

AND 

PNEUMATICS. 


CHAMBERS’  EDUCATIONAL  COURSE. 


INTRODUCTORY  OBSERVATIONS 


BT 

THE  AMERICAN  EDITOR. 


With  this  third  book  of  Natural  Philosophy,  the  teacher 
will  be  able  to  conduct  his  pupils  to  an  easy  acquaintance 
with  the  most  intricate  ar^l  difficult  features  in  the  whole  sci- 
ence, the  two  former  books  having  removed  every  obstacle  in 
the  way  of  the  learner.  The  laws  of  matter  and  motion,  and 
the  elements  of  practical  machinery,  and  moving  forces  with 
reference  to  solids,  having  been  made  plain,  the  laws  of  fluids 
will  much  more  readily  be  understood  than  if  previously 
studied. 

Hydrostatics,  or  the  science  of  fluids  at  rest;  Hydraulics,  or 
the  science  of  fluids  in  motion;  and  Pneumatics,  or  the  science 
of  air  and  gaseous  fluids,  are  the  successive  topics  of  this 
volume.  Their  kindred  character  and  striking  analogies  ren- 
der them  appropriate  subjects  to  be  considered  together,  while 
their  great  practical  importance  in  domestic  economy  and  the 
business  of  life,  would  seem  to  commend  them  to  young 
people,  as  having  special  claims  upon  their  attention. 

The  catechetical  questions  on  every  page  will  be  found  to 
be  thoroughly  analytical  of  the  entire  volume,  and  the  answer 
should  be  required  in  the  words  of  the  text  at  first,  and  after- 
wards expressed  in  other  terms,  and  with  other  illustrations 
than  those  found  in  the  book.  For  this  purpose,  the  teacher 
should,  in  his  discretion,  vary  the  questions  and  call  for  other 
examples. 

A class  thus  instructed  will  be  able  to  exhibit  proofs  of 

3 


4 


INTRODUCTORY  OBSERVATIONS. 


their  actual  knowledge  in  these  departments,  by  once  going 
through  this  book,  which  at  an  exhibition  would  astonish 
those  who  should  witness  it,  without  being  acquainted  with 
the  facilities  which  this  volume  furnishes  to  the  learn;r  by  its 
simplicity  and  skilful  adaptation  to  the  juvenile  mind. 

With  such  views,  it  is  earnestly  recommended  to  the  prac- 
tical teachers  of  our  common  schools,  by 

The  American  Editor. 


PREFACE. 


The  present  Treatise,  comprehending  Hydrostatics  and 
Hydraulics  (or,  conjointly,  Hydrodynamics),  also  Pneuma- 
tics, forms  the  third  department  in  Natural  Philosophy. 

The  Pupil,  having  been  made  acquainted  with  the  Laws  of 
Matter  and  Motion  and  with  Mechanics,  is  now  introduced  to 
a knowledge  of  the  Laws  of  Fluids,  both  as  respects  liquid 
and  aeriform  bodies.  By  uniting  Hydrostatics,  Hydraulics, 
and  Pneumatics,  in  one  treatise,  the  whole  subject  of  fluids  is 
at  once  brought  before  the  mind,  and  is  thereby  calculated  to 
make  a more  forcible  and  agreeable  impression,  than  if,  as 
according  to  custom,  it  were  divided  into  separate  books. 

In  this,  as  in  the  preceding  treatises,  very  great  pains  have 
been  taken  to 'render  the  language  simple  and  intelligible,  so 
that  the  learner  may  find  at  least  no  technical  difficulty  in  his 
path.  The  sentences  and  paragraphs  are  likewise  written  and 
arranged  in  such  a manner  as  to  form  a progressive  series  of 
distinct  propositions,  relieved  from  extraneous  verbiage,  and 
suitable  alike  for  the  study  of  the  Pupil,  and  as  the  subject 
of  a searching  examination  by  the  Master. 


. t 


: V : > - : 


• • . > 


_ 

' 

■ 


■ 


CONTENTS. 


Page 

H tdrostatics  and  Hydraulics 9 

General  Definitions 9 

Hydrostatics 11 

Pressure  Equal  in  all  Directions 12 

Pressure  in  Proportion  to  Height 13 

Equal  Levelness  of  Surface 23 

Levels 25 

Specific  Gravity 28 

Fluid  Support 30 

Hydrometers 38 

Hydraulics 40 

Water,  a Mechanical  Agent 40 

Aqueducts — Fountains 43 

Springs 45 

Friction  between  Fluids  and  Solids 46 

Action  of  Water  in  Rivers 49 

Waves 50 

• Alteration  of  Temperature 51 

Pneumatics 53 

General  Definitions 53 

The  Atmosphere 57 

Laws  of  Air 58 

Pressure  of  Air 59 

The  Air-pump 63 

Pressure  of  Air  on  Solids  and  Liquids 66 


7 


CONTEXTS. 


8 


Pneumatics.  Page 

Pressure  on  Mercury — the  Barometer 68 

Pressure  on  Water — Pumps 72 

Syphons 74 

Syphon  Springs 76 

Boilding  Point  determined  by  Atmospheric  Influence  78 

Steam 80 

Latent  Heat 81 

Alteration  of  Temperature  in  Air 85 

Air  in  Motion — Winds 88 

Sea  and  Land  Breezes 90 

Ventilation ; 92 

The  Diving-bell 100 

Buoyant  Property  of  Aeriform  Fluids 102 

Balloons 104 


NATURAL  PHILOSOPHY 


HYDROSTATICS  AND  HYDRAULICS. 


GENERAL  DEFINITIONS. 

1 . Matter  exists  in  three  principal  forms — solid,  liquid, 
and  gaseous  or  aeriform.  These  forms  respectively,  and  the 
various  modifications  of  them,  are  the  immediate  result  of 
certain  principles  of  attraction  and  repulsion  operating  on 
the  atoms  or  particles  of  which  matter  is  composed.* 

2.  The  solid,  liquid,  and  aeriform  varieties  of  matter, 
assume  a position  on  our  globe  corresponding  to  their 
heaviness  or  density  in  a given  volume — the  solid  sinks 
lowest,  and  composes  the  chief  mass  of  the  earth ; above 
the  solid  lies  the  liquid  variety,  in  the  form  of  the  ocean, 
rivers,  and  lakes ; and  above  all  is  the  atmosphere,  con- 
sisting of  an  expanse  of  aeriform  matter,  which  wraps  the 
whole  earth  round  to  an  elevation  of  from  forty-five  to 
fifty  miles  above  the  highest  mountains.  In  this  great 
ocean  of  air,  loaded  less  or  more  with  particles  of  mois- 
ture from  the  liquids  beneath,  we  live,  breathe,  and  move, 
and  plants  grow  and  receive  an  appropriate  nourishment. 

3.  Though  differing  both  in  substance  and  appearance, 
the  liquid  and  aeriform  varieties  of  matter  resemble  each 

* The  principles  of  attraction  and  repulsion  are  explained  in  the 
Laws  of  Matter  and  Motion,  from  paragraph  34  to  i24,  and  must 
be  already  familiar  to  the  pupil.  As  forming  the  basis  of  physical 
science,  they  ought  to  be  thoroughly  understood. 


1 In  how  many  forms  does  matter  exist? 

2.  How  are  they  arranged  in  the  globe  ? 

9 


V 


10 


GENERAL  DEFINITIONS. 


other  in  many  of  their  properties  and  tendencies,  and  con- 
stitute the  class  of  bodies  termed  fluids. 

4.  Fluids  signify  bodies  which  will  flow,  or  whose  com- 
ponent particles  are  easily  moved  among  each  other. 

5.  Some  fluids  are  so  thick  and  viscous,  or  sticky,  that 
they  can  scarcely  flow,  as  tar,  honey,  and  some  metais  in 
a state  of  fusion  ; others  flow  with  ease,  as  water  and  dis- 
tilled spirits  ; while  others  are  so  light  and  volatile,  as  to 
be  impalpable  to  the  touch  and  invisible  to  the  eye,  as  pure 
atmospheric  air  and  various  gases. 

6.  It  is  common  to  divide  fluids  into  two  kinds — non- 
elastic fluids  and  elastic  fluids ; that  is,  fluids  which  can- 
not be  compressed  into  a smaller  bulk,  and  those  which 
are  susceptible  of  compression.  The  non-elastic  fluids  are 
Water  and  all  other  varieties  of  liquid  bodies  ; but  recent 
experiments  prove  that  the  term  is  not  strictly  applicable 
to  them.  It  has  been  found  that  water  may  be  compressed 
in  a confined  vessel,  to  a small  extent,  by  means  of  a very 
great  pressure,  and  it  is  certain  that  water  at  a considera- 
ble depth  in  the  ocean  is  more  dense  or  compressed  than 
at  the  surface  ; water,  consequently,  is  an  elastic  substance  ; 
but  as  it  can  be  compressed  only  with  very  great  difficulty, 
the  term  non-elastic  fluid  is  not  altogether  inappropriate. 

7.  Atmospheric  air  and  all  gases  are  elastic.  They 
can,  with  little  difficulty,  be  compressed  into  a much  small- 
er volume  than  they  ordinarily  ’possess  ; and  when  the 
pressure  is  removed,  they  return  to  their  original  bulk. 
Some  gases  may  be  compressed  to  such  an  extent  as  to  as- 
sume the  form  of  liquids  and  solids;  in  other  words,  from 
the  condition  of  being  perfectly  invisible  to  the  eye,  they 
can  be  made  to  appear  as  a piece  of  solid  matter,  which 
may  be  touched  and  handled. 

8.  In  treating  the  subject  of  fluids,  it  is  convenient  to 
refer  in  the  first  place  to  those  which  are  of  the  liquid 
form,  and  afterwards  to  those  which  are  elastic  or  aeri- 
form. 


3.  Define  fluids,  and  their  variety. 

4.  How  are  fluids  divided  ? and  what  of  compressibility  ? 

5.  Name  the  peculiarities  of  elastic  fluids. 


HYDROSTATICS.  1 1 

9.  Pure  water,  at  an  ordinary  temperature,  furnishes  the 
most  suitable  example  of  liquid  bodies. 

10.  Water  also  gives  the  name  of  the  department  of 
science  which  includes  the  laws  of  liquids.  Thus,  Hy- 
drostatics, from  two  Greek  words  signifying  ivater  and 
to  s add , treats  of  the  weight,  pressure,  and  equilibrium  of 
liquids  in  a state  of  rest;  and  Hydraulics,  from  two 
Greek  words  signifying  ira'er  and  a pipe,  treats  of  liquids 
in  motion,  and  the  artificial  means  of  conducting  liquids  in 
pipes,  or  raising  them  by  pumps. 


HYDROSTATICS. 

11.  In  ancient  times  water  was  believed  to  be  an  ele- 
ment or  simple  substance  in  nature.  It  is  now  ascertained 
by  experiment  that  water  is  not  an  elementary  body,  but 
is  a substance  composed  chiefly  of  two  gases  in  a state  of 
chemical  union,  and  into  these  gases  it  can  be  resolved  by 
an  artificial  process.  The  investigation  of  this  subject  be- 
longs to  Chemistry. 

12.  As  a liquid,  water  consists  of  exceedingly  small 
particles  or  atoms  of  matter  in  mechanical  combination. 

Id.  The  exact  nature  and  form  of  the  atoms  compos- 
ing water  are  not  satisfactorily  known,  in  consequence  of 
their  exceeding  smallness.  They  may  be  compared  to 
very  small  particles  of  sand,  cohering  slightly,  and  easily 
slipping  or  sliding  over  each  oth  r.  Whatever  may  be 
the  nature  and  form  of  these  exquisitely  fine  atoms,  it  is 
certain  that  they  can  adhere  firmly  together  so  as  to  as- 
sume the  form  of  a solid,  as  in  the  case  of  ice  ; and  be 
made  to  separate  from  each  other,  and  disperse  through 
the  thinner  fluid  of  the  atmosphere,  in  the  forms  of  steam, 
clouds,  or  mist. 

14.  Thus,  IMPERFECT  COHESION  OF  ATOMS  OR  PARTICLES 
is  a property  common  to  all  fluids. 


6.  Define  Hydrostatics  and  Hydraulics. 

7.  What  of  the  composition  of  water? 

8.  What  of  the  atoms  of  water  and  their  changes  of  form  f 


12 


HYDROSTATICS. 


15.  The  atoms  composing  water,  being  in  closer  union 
than  those  of  air,  are  observable  as  a mass,  and  palpable  to 
the  touch.  When  the  hand  is  dipped  into  them,  and  then 
withdrawn,  a certain  quantity  of  the  atoms  is  brought 
away  on  the  surface  of  the  skin  ; and  this  adhesion  of  the 
particles  of  water  (caused  by  attraction  of  cohesion)  is 
what  we  in  ordinary  language  call  wetness.  Certain  sub- 
stances, as  is  well  known,  absorb  water  to  a great  extent ; 
in  such  cases,  the  minute  particles  of  the  water  merely  pene- 
trate and  fill  up  the  crevices  in  the  substance. 


PRESSURE  EQUAL  IN  ALL  DIRECTIONS. 

15.  Solid  bodies,  as  a stone,  or  piece  of  metal,  or  wood, 
have  a natural  tendency  to  press  only  in  one  direction,  that 
is  downwards,  or  in  the  direction  of  the  earth’s  centre,  in 
obedience  to  the  law  of  terrestrial  attraction. 

17.  Water  has  a similar  natural  tendency  to  press  down- 
wards, and  from  the  same  cause  ; as  for  example,  when  a 
jug  of  water  is  spilled,  the  water  is  seen  to  fall  in  a stream 
to  the  ground. 

18.  Water,  however,  is  governed  by  a law  of  pressure, 
independently  of  this  general  law  of  gravitation.  This 
peculiar  or  independent  law  consists  of  the  tendency  in 
the  particles  of  any  mass  of  water  to  press  equally  in  all 
directions. 

19.  Pressure  equally  in  all  directions  may  be  con- 
sidered as  the  first  or  great  leading  law  in  reference  to 
water,  and  generally  all  fluids,  liquid  and  gaseous. 

20.  The  pressure  equally  in  all  directions  is  a result  of 
the  exceeding  smallness  of  the  individual  particles,  and  of 
the  perfect  ease  with  which  they  glide  over  or  amongst 
each  other. 

, 21.  l'ot  exemplify  equal  pressure,  fill  a leathern  bag 

witk’1  water/'  ani  then  s£& miY’thb  rfibhrth  of  the  bag  so 

.abiiifr ii;;  a,  nomn.oo 


. Give  an  example  of  their  cohesion,  ; 
10.  How  is  gravitaiion,y\o,cfi^pd|jp)w^tej  l 


, is  g r a v a a.  .orL  6p , wa,tef  ? . H ,rl 

H.  What  is  ihe  law.ojgjr^s^^p^Il  fJuids.f  , . ,-rj  - 

jVgfim  l ,m  . a 

13.  Explain  the  example  cited. 


PRESSURE  IN  PROPORTION  TO  HEIGHT.  13 

closely  that  none  of  the  water  can  escape.  Now,  squeeze 
or  press  upon  the  bag  so  as  almost  to  make  it  burst.  The 
pressure  so  applied  does  not  merely  act  upon  the  water 
immediately  under  the  point  of  pressure,  but  acts  equally 
upon  every  particle  of  water  in  the  mass — the  particles  at 
the  centre  being  as  much  pressed  upon  as  those  at  the  out- 
side ; and  it  will  be  observed  that  the  water  will  squirt  out 
with  equal  impetuosity  at  whatever  part  you  make  a hole 
in  the  surface. 

23.  In  this,  as  in  all  similar  cases,  there  is  a transmis- 
sion of  pressure  throughout  the  mass.  Each  particle 
presses  on  those  next  it ; and  so,  by  the  force  communicat- 
ing from  particle  to  particle,  the  whole  are  equally  affected. 

23.  In  the  case  of  water  lying  at  repose  in  an  open  ves- 
sel, the  tendency  to  press  equally  in  all  directions  is  not 
observed  to  act  upward,  because  the  gravity  of  the  mass 
k eps  the  water  down  ; but  on  pressing  upon  the  surface 
of  the  liquid,  we  observe  that  it  rises  against  the  compres- 
sion, or  tries  to  escape  in  any  way  it  can.  To  take  another 
example — if  we  plunge  our  hand  into  a vessel  of  water, 
we  displace  so  much  liquid,  and  cause  it  to  rise  higher  up 
the  sides  of  the  vessel.  In  this  case,  the  water  is  observed 
to  rise  without  any  reluctance  ; it  as  readily  presses  up- 
ward as  downward. 

PRESSURE  IN  PROPORTION  TO  HEIGHT. 

24.  Although  it  is  a property  in  fluids  to  press  equally 
in  all  directions,  the  degree  of  intensity  of  pressure  in  any 
mass  of  fluid  is  estimated  by  the  vertical  height  of  the 
mass,  and  its  area  at  the  base. 

25.  Pressure  of  water  in  proportion  to  its  verti- 
cal height  and  its  area  at  the  base,  is  therefore  a 
second  leading  feature  in  the  laws  of  water. 

2(3.  In  other  words,  the  pressure  of  a column  of  water 
does  not  depend  on  the  width  or  thickness  of  the  column, 
but  on  its  height  and  extent  of  its  base  or  lower  part. 


14.  Whai  other  illustrations  are  given  ? 

15.  H.av  is  tiie  degree  ol  p-eesure  estimated? 


14 


HYDROSTATICS. 


27.  The  whole  of  any  fluid  mass  may  be  imagined  to 
consist  of  a number  of  columns  of  an  inconsiderable  thick- 
ness, which  stand  perpendicularly  on  the  horizontal  base  of 
the  containing  vessel,  and  press  the  base  of  the  vessel  with 
their  respective  weights.  The  pressure,  then,  if  the 
height  of  the  fluid  be  the  same  throughout,  is  as  the  num- 
ber of  columns,  and  this  number  is  according  to  the  area 
of  the  base.  Consequently,  in  vessels  whose  bases  differ 
as  to  area,  and  which  contain  fluids  of  the  same  density, 
but  different  heights,  the  pressure  will  be  in  the  compound 
ratio  of  the  bases  and  heights. 

28.  If  the  columns  of  which  a fluid  mass  was  supposed 
to  consist,  were  formed  of  particles  lying  in  perpendicular 
lines,  the  pressure  of  the  fluid  would  be  exerted  on  the 
bottom  of  the  vessel  only  ; but  as  they  are  situated  in 
every  irregular  position,  there  must  of  consequence  be  a 
pressure  exerted  in  every  direction  ; which  pressure  must 
be  equal  at  equal  depths.  For  if  any  part  of  the  whole  mass 
were  not  equally  pressed  on  all  sides,  it  would  not  move 

towards  the  side  on  which  the  pressure 
was  least,  and  would  not  become  qui- 
escent till  such  equal  pressure  was  ob- 
tained. The  quiescence  of  the  parts 
of  fluids  is  therefore  a proof  that  they 
are  equally  pressed  on  all  sides.* 

29.  Several  interesting  experiments 
maybe  made  to  prove  that  the  pressure 
of  water  is  in  proportion  to  its  height 
and  width  of  base. 

30.  Figure  1 represents  two  vessels 
of  equal  height,  the  same  width  of  base, 
but  of  different  shapes  otherwise.  One, 
AB,  is  of  equal  thickness  from  bottom 
to  top  ; the  other,  CD.  is  a tall  narrow 
tube  connected  with  a broad  base.  If 

* These  definitions,  in  paragraphs  27  and  28,  are  given  by  Nichol- 
son, in  his  Introduction  to  Natural  Philosophy. 


ill  -D 


Fig.  1. 


16.  What  method  of  calculation  is  named  ? 

17.  What  does  the  quiescence  of  fluids  prove  ? 


PRESSURE  IN  PROPORTION  TO  HEIGHT. 


15 


Doth  be  filled  with  water  to  the  same  height,  the  pressure 
upon  any  part  of  the  sides  of  either  will  be  alike  power- 
ful. The  pressure  against  the  inside  of  the  narrow  tube 
at  C will  be  as  great  as  against  the  inside  of  the  much  wider 
tube  at  A — the  mere  width  of  column  making  no  differ- 
ence in  the  degree  of  pressure. 

31.  Another  example. — Fi- 
gure 2 represents  a vessel  with 
a broad  top  EE,  tapering  to  a 
narrow  base  CD.  The  dotted 
enclosure  ABCD  represents  an 
ideal  column  of  water  the  width 
of  the  base.  The  vessel  is  sup- 
posed to  be  filled  with  water  to 
the  surface  EE.  Yet  the  base 
or  bottom  sustains  no  more  pres- 
sure than  that  described  by  the  ideal  colujnn  ABCD;  for 
the  other  parts  of  the  contained  fluid  can  only  press  the 
column  ABCD,  and  also  the  sloping  sides  laterally,  and 
therefore  do  not  contribute  to  the  increase  of  the  weight 
or  {Pressure  on  the  bottom  CD. 

32.  If  we  take  a vessel  of  the 
same  capacity,  but  with  a broad 
base,  as  in  Figure  3,  the  pres- 
sure on  the  bottom  is  very  dif- 
ferent. In  this  case  the  base 
EF  sustains  a pressure  equal  to 
the  weight  of  a column  whose 
base  is  EF,  and  height  equal  to 
AC  ; for  the  water  in  the  central 
column  ABCD  presses  laterally 
or  sidewise,  with  the  same  force  as  it  does  on  the  part  on 
which  it  stands,  and  thus  an  uniformity  of  pressure  is  es- 
tablished over  every  part  of  the  bottom. 

33.  From  these  two  cases  combined,  the  reason  is  evi- 
dent why  fluids  contained  in  the  several  parts  of  vessels 
remain  everywhere  at  the  same  height ; for  the  low- 


A B 


18.  Explain  the  diagrams,  and  the  principle  of  each. 

19.  What  of  the  first  diagram  ? 


16 


HYDROSTATICS. 


est  part  where  they  communicate  may  be  regarded  as  the 
common  base ; and  the  fluids  which  rest  thereon  are  in 
equilibrio  then  only,  when  their  heights  are  equal,  how- 
ever their  quantities  may  vary. 

34.  We  may  prove  the  truth  of  these  propositions  in 
various  ways.  Let  ABCD,  Figure  4,  re- 
present a cylindrical  vessel,  to  the  inside 
of  which  is  fitted  the  cover  G,  which,  by 
means  of  leather  at  the  edge,  will  easily 
slide  up  and  down  in  the  internal  cavity, 
without  permitting  any  water  to  pass  be- 
tween it  and  the  surface  of  the  cylinder. 
In  the  cover  is  inserted  the  small  tube  EF, 
open  at  top.  and  communicating  with  the  in- 
side of  the  cylinder  below  the  cover  of  G. 
The  cylinder  is  filled  with  water,  and  the 
cover  put  on.  Then,  if  the  cover  be  load- 
ed with  the  weight,  suppose  of  a pound,  it 
will  be  depressed,  the  water  will  rise  in  the 
tube  to  E,  and  the  weight  will  be  sustained. 
In  other  words,  a very  small  quantity  of 
water  in  this  narrow  tube  will  press  with 

a force  as  great  as  if  the  vessel  were  of  the  dimensions 
KLCD,  instead  of  ABCD.  By  filling  the  tube  to  F,  a 
force  will  be  gained  sufficient  to  balance  additional  pound 
weights  on  the  cover  G,  and  as  great  as  could  be  conferred 
by  a vessel  of  equal  breadth  all  the  way  up  to  F. 

35.  Water,  in  its  pressure  equally  in  all  directions, 
presses  upwards  as  well  as  downwards.  This  is  seen  in 
the  above  experiments.  Take  Figure  4 as  an  example. 
The  water  in  the  vessel  ABCD,  when  the  tube  is  filled, 
presses,  as  has  been  said,  with  a force  equal  to  that  of  a 
column  of  water  of  equal  breadth  all  the  way  up  to  F. 
This  can  only  be  in  consequence  of  the  water  in  the  ves- 
sel ABCD  pressing  violently  upwards  against  the  cover 
G,  which  violence  causes  a corresponding  reaction  on  the 
bottom  of  the  vessel.  This  reaction,  then,  is  equivalent  to 


E 


Fig.  4. 


20.  How  is  the  equilibrium  of  fluids  explained  ? 

21.  Explain  the  next  diagram,  and  its  use. 


PRESSURE  IN  PROPORTION  TO  HEIGHT. 


17 


v>  rtical  height.  To  use  a figure  of  speech,  the  water  in 
the  vessel  is  in  the  condition  of  a man  pressing  equally  up- 
wards with  his  shoulders  and  downwards  with  his  feet  at 
the  same  time ; and  the  more  he  is  acted  upon  by  weight 
above,  the  more  powerfully  does  he  exert  his  pressure  in 
both  directions. 

36.  The  great  force  which  may  be  exerted  by  a small 
but  high  column  of  water,  is  further  exempli- 
fied by  a tube  of  from  twenty  to  thirty  feet  in 
length-  fitted  into  the  end  of  a cask,  as  in 
Figure  5.  One  pouring  in  water  sufficient  to 
fill  the  cask,  and  also  the  tube  to  its  summit, 
so  great  a strain  will  be  made  on  the  hoops 
of  the  vessel,  that  it  will  in  all  likelihood  burst ; 
in  effect,  the  pressure  on  the  sides  of  the  cask 
will  be  equal  to  that  of  a column  as  wide  as 
the  cask  and  as  high  as  the  tube ; and  for  this 
degree  of  pressure,  casks  are  not  usually  pre- 
pared. If  we  suppose  that  the  area  of  the 
tube  be  no  more  than  the  twentieth  of  an  inc  , 
and  the  tube  altogether  contain  only  a pound 
of  water,  the  pressure  caused  by  this  incon- 
' »•  siderable  quantity  of  liquid  will  be  equal  to  a 
pound  on  every  twentieth  of  an  inch  in  the  cask  ; and  for 
this  enormous  degree  of  pressure,  no 
cask  is  prepared. 

37.  An  instrument  called  the  hy- 
drostatic bellows  has  been  constructed 
to  exemplify  the  effect  produced  by  the 
pressure  of  a small  column  of  water. 
As  represented  in  Figure  6,  it  consists 
of  two  circular  stout  boards  connected 
together  with  leather,  in  the  form  of  a 
pair  of  strong  bellows.  A tube  A 
communicates  with  the  interior  between 
the  boards.  Supposing  the  instrument 
to  be  strong  enough,  a person  standing 
Fig.  e.  on  the  upper  board  may  raise  himself 

22.  How  is  the  upward  pressure  of  water  shown  ? 

23  How  may  the  force  of  a small  column  of  water  be  exemp  ified  I 


18 


HYDROSTATICS. 


by  pouring  water  into  the  tube,  and  filling  it  along  with 
the  bellows.  It  is  usual  to  estimate  the  pressure  by 
means  of  weights,  W.  If  the  tube  hold  an  ounce  of  water, 
and  has  an  area  equal  to  a thousandth  part  of  the  area  of 
the  top  of  the  bellows,  one  ounce  of  water  in  the  tube 
will  balance  a thousand  ounces  placed  in  the  bellows. 

38.  This  remarkable  property  in  liquids,  which  is  called 
the  Hydrostatic  paradox,  is  analogous  in  principle  to  that 
which  in  mechanics  is  called  the  Law  of  Virtual  Veloci- 
ties.* According  to  this  fundamental  rule — a small  weight 
descending  a long  way,  in  any  given  length  of  time,  is 
equal  in  effect  to  a great  weight  descending  a proportion- 
ally shorter  way  in  the  same  space  of  time.  The  rule,  as 
applied  to  liquids,  may  be  stated  thus  : — A small  quantity 
of  water  descending  in  a long  column  is  equal  in  effect  to 
a proportionately  great  pressure  exerted  by  a large  volume 
of  water  in  a short  column. 

39.  The  law  of  pressure  in  proportion  to  height  of 
column  is  shown  in  the  annexed  re- 
presentation, Figure  7,  of  a vessel 
with  an  uniformly  level  base  and  full 
of  water.  Dividing  the  depth  into 
10  equal  sections,  to  represent  feet, 
as  marked  from  1 to  10,  it  is  found, 
that,  at  the  depth  of  1,  there  is  a pres- 
sure of  one  foot  of  water,  at  2,  two  feet,  and  so  on  to  10 
at  the  bottom,  where  there  is  a pressure  of  ten  vertical 
feet  of  water.  The  average  pressure  of  the  whole  is  at 
the  middle,  at  5.  These  degrees  of  intensity  of  pressure 
have  no  reference  to  the  horizontal  breadth  or  length  of 
the  mass.  The  same  pressure  is  sustained,  whether  the 
vessel  be  a foot  or  a mile  in  breadth. 

40.  As  in  this  example,  whatever  deficiency  of  pres- 
sure there  is  upon  the  perpendicular  sides  of  a vessel  of 
water  above  the  middle  or  point  of  average  pressure,  is 

* See  Mechanics,  paragraph  16  to  27. 


24.  Describe  the  hydrostatic  bellows,  and  its  results. 

25.  Dofine  the  hydrostatic  paradox. 

26.  Explain  the  diagram. 


PRESSURE  IN  PROPORTION  TO  HEIGHT.  10 

compensated  by  a corresponding  excess  of  pressure  be- 
neath the  middle ; consequently,  the  entire  pressure  dif- 
fused over  the  sides  is  equal  to  that  at  the  middle  or  point 
of  average  pressure.  A perpendicular  side  of  a cubical 
vessel,  according  to  this  statement,  sustains  a lateral  pres- 
sure precisely  equal  to  the  half  of  that  which  is  endured  by 
the  bottom. 

41.  We  may  calculate  the  degree  of  lateral  pressure  in 
vessels  having  perpendicular  sides  and  flat  horizontal  bot- 
toms, by  fir-t  finding  the  number  of  square  feet  in  the  sides 
below  the  surface  of  the  liquid  ; then  multiplying  that  by  the 
number  of  feet  in  half  the  depth  of  the  liquid;  by  which 
calculation,  the  product  will  express  the  number  of  solid 
feet  of  the  liquid,  whose  weight  is  equal  to  the  lateral  pres- 
sure. We  may  find  the  number  of  square  feet  in  the  sides, 
by  multiplying  the  number  of  feet  in  the  circumference  of 
the  bottom  by  the  number  of  feet  in  the  depth  of  the  liquid. 

42.  Example. — To  find  the  degree  of  pressure  on  the 
perpendicular  sides  of  a vat  24  feet  deep  from  the  surface 
of  the  liquid,  and  40  feet  in  circumference — Multiply  the 
24  by  40,  and  the  product  96  ) gives  the  area  of  the  sides  ; 
then  multiply  the  960  by  half  the  height,  that  is  12,  and 
the  product  is  11,520  cubic  feet  of  water,  or  the  volume 
of  liquid  whose  weight  is  equal  to  the  pressure  on  the  sides. 
We  next  find  the  weight  per  cubic  foot,  which  is  reckoned 
to  be  1000  ounces  ; then  11,520  multiplied  by  1000,  gives 
11,520,000  ounces,  which  is  the  pressure  of  the  water  on 
the  sides. 

43.  In  consequence  of  the  pressure  of  liquids  being  as 
the  vertical  height  and  area  of  the  base,  it  may  happen 
that  the  lateral  pressure  on  the  sides  of  a containing  vessel 
is  greater  than  the  whole  weight  of  the  liquid  ; this  will 
be  the  case  when  the  surface  of  the  sides  in  contact  with 
the  liquid  exceeds  the  ratio  of  double  the  magnitude  of  the 
bottom — at  double  the  magnitude,  both  lateral  and  perpen- 
dicular pressures  are  alike,  and  each  is  equal  to  the 
weight  of  the  liquid. 


27.  What  of  the  lateral  pressure  ? 

28.  How  may  it  be  calculated  ? 

29  State  the  example  and  its  result. 


20 


HYDROSTATICS. 


44.  The  circumstance  of  pressure  increasing  in  propor- 
tion to  depth,  suggests  the  valuable  practical  lesson  of 
greatly  increasing  the  breadth  of  embankments  for  dams 
and  canals  from  the  top  downwards,  so  as  to  give  much 
greater  strength  to  the  base  than  the  summit ; also  of 
increasing  the  strength  of  the  lower  hoops  of  large  vats  to 
prevent  their  bursting.  It  likewise  demonstrates  the  pro- 
priety of  making  dams,  ponds,  canals,  and  vessels  for 
liquids  generally,  as  shallow  as  is  consistent  with  con- 
venience or  their  required  purpose.  In  each  case  it  is 
important  to  recollect  that  the  degree  of  pressure  on  the 
sides  is  irrespective  of  shape  or  size  of  the  contents,  and 
depends  exclusively  on  the  height  of  the  liquid  from  its 
upper  surface  to  its  base. 

45.  That  pressure  in  water  is  not  according  to  the  volume, 
but  the  height  above  the  point  of  pressure,  is  obvious  from 
many  facts  both  in  nature  and  art.  Whether  we  plunge 
an  object  a foot  deep  in  the  ocean  or  in  a jar  of  water,  the 
pressure  upon  it  is  the  same.  The  mere  extent  of  the 
volume  of  liquid  is  of  no  consequence.  Therefore,  a pre- 
cipitous shore  press  d upon  by  the  sea  to  the  height  of 
any  given  number  of  feet,  suffers  no  more  pressure  (sup- 
posing the  sea  to  be  at  rest)  than  the  side  of  a canal  of  the 
same  number  of  feet  in  height. 

46.  If  the  law  of  pressure  of  fluids  were  otherwise  than 
that  now  stated,  no  species  of  embankment,  no  strength  of 
shore,  could  withstand  the  pressure  of  the  ocean,  particu- 
larly in  a high  state  of  the  tide.  In  consequence  of  the 
law  of  pressure  being  simply  as  the  vertical  height,  we 
are  enabled  by  artificial  means  to  stem  the  volume  of  a 
far-spreading  ocean,  and  to  secure  the  dry  land  from  its 
invasion.  A knowledge  of  this  important  law  might 
induce  the  attempt  to  secure  many  thousands  of  acres  of 
land  which  are  now  covered  by  the  tide. 

47.  If  a vessel,  as  for  instance  a barrel,  be  filled  with 
water,  and  three  apertures  be  made  in  its  side  at  different 


30.  How  may  the  lateral  pressure  exceed  the  whole  weight  ? 

31.  What  practical  uses  of  this  principle  are  named  ? 

32.  What  facts  in  nature  are  reierred  to  in  prooft 


PRESSURE  IN  PROPORTION  TO  HEIGHT.  21 

heights,  as  in  Figure  8,  the  liquid  will  pour  out  with  an 
impetuosity  corresponding  to  the  depth  of  the  aperture 

from  the  top.  The  jet  A 
nearest  the  top  of  the  bar- 
rel, having  little  pressure 
above  it,  will  be  projected 
but  a short  way ; the  jet 
B,  having  a greater  pres- 
sure, will  perhaps  go  to 
double  the  distance ; and 
the  jet  C,  having  the  great- 
est pressure  of  all,  will  go 
to  a greater  distance  still. 
Jets  of  this  kind  obey  the  laws  which  govern  solid  projec- 
tiles in  their  flight;*  they  describe  a curvilinear  motion, 
the  width  of  curve  being  proportioned  to  the  impressed 
force. 

48.  Practically,  the  discharge  of  liquids  from  apertures 
is  partly  affected  by  the  shape  and  width  of  the  aperture  ; 
for  water  is  retarded  by  friction,  and  by  its  own  impetu- 
osity or  cross  currents  in  a small  channel. 

49.  It  is  reckoned  that  the  pressure  of  water  on  any 
body  plunged  into  it,  or  on  the  bottom  or  sides  of  the 
containing  vessel,  is  about  one  pound  on  the  square  inch 
for  every  two  feet  of  the  depth. 

50.  Pieces  of  wood  sunk  to  great  depths  in  the  ocean 
become  so  saturated  with  water  by  the  pressure  of  the 
superincumbent  mass,  that  they  lose  their  buoyancy,  and 
remain  at  rest  at  the  bottom.  The  depth  to  which  divers 
can  descend  is  limited  by  the  increased  pressure  they 
experience  in  their  descent.  If  a bottle  be  firmly  corked 
and  sealed,  and  sunk  to  a great  depth  in  the  ocean,  the 
cork  will  either  be  forced  in  or  the  bottle  broken  by  the 
pressure.  An  air-bell  rising  from  a depth,  expands  as  it 

* See  Laws  of  Projectiles,  paragraph  237,  &c.,  Laws  of  Matter 
and  Motion. 


33.  Explain  the  diagram  and  the  laws  it  exhibits. 

34.  How  is  water  retarded,  and  what  the  ratio  of  pressure  ? 

35.  What  examples  of  pressure  are  named  ? 


22 


HYDROSTATICS. 


approaches  the  surface.  At  the  depth  of  a thousand 
fathoms,  water  is  estimated  to  be  about  a twentieth  part 
more  dense  in  the  hulk  than  at  the  surface. 

51.  The  great  effects  that  may  take  place  by  the  action 
of  a small  but  high  column  of  water,  are  sometimes  exem- 
plified in  the  rending  of  mountains.  In  Figure  9,  a 
mountain  or  high  rocky  knoll  is  represented,  with  a small 
vertical  crevice  A reaching  from  the  summit  to  an  inter- 
nal reservoir  of  water  near  the  base.  If  there  be  no 
means  of  outlet  to  the  liquid,  and  if  rain  continue  to  keep 
the  crevice  and  its  terminating  reservoir  full,  the  lateral 


force  exerted  by  the  upright  column  will  be  very  consi- 
derable. Supposing  the  crevice  to  be  an  inch  in  diameter, 
and  two  hundred  feet  deep,  the  pressure  would  be  equal 
to  nearly  a half  a ton  on  every  square  inch ; such  a force 
continually  acting  on  the  sides  of  the  mountain  (laying 
out  of  view  the  great  additional  force  given  by  expansion 
of  the  liquid  in  freezing  during  winter)  would  probably 
in  time  overcome  the  cohesiveness  of  the  mass,  and  burst 
the  whole  asunder.  In  this  property  in  water,  therefore, 
we  see  one  of  the  many  provisions  of  nature  for  producing 
changes  on  the  surface  of  the  earth. 

52.  Effects  of  a similar  character,  but  on  a less  scale, 
are  observable  in  the  bursting  of  walls  behind  which  earth 


36.  Explain  the  diagram  and  its  design. 

37.  What  phenomena  are  thus  explained? 

38.  What  results  from  the  mobility  of  the  atoms  of  ater  ? 


EQUAL  LEVELNESS  OF  SURFACE. 


23 


has  been  piled,  and  in  which  no  proper  outlets  for  water 
have  been  provided ; as  also  in  the  bursting  upwards 
of  drains  upon  a declivity,  when  they  become  choked. 

HYDROSTATICS  CONTINUED. 

EQUAL  LEVELNESS  OF  SURFACE. 

53.  On  account  of  the  perfect  ease  with  which  particles 
of  water  move  over  or  among  each  other,  a quantity  or 
mass  of  them  can  have  no  solidity,  firmness,  or  tenacity  ; 
accordingly,  any  such  mass  readily  accommodates  itself 
to  the  shape  of  any  vessel  or  natural  hollow  in  which  it 
may  be  placed  ; the  mass  takes  the  form  of  the  vessel  or 
hollow,  whatever  it  may  be. 

54.  While  the  easy  motion  of  the  particles  among  each 
other  causes  them  to  accommodate  themselves  to  the 
shape  of  any  vessel,  the  force  of  gravity  causes  them  at 
the  same  time,  to  seek  the  lowest  level  for  repose.  Each 
particle  tries  to  get  as  low  as  it  can.  The  result  of  this 
general  tendency  throughout  the  mass  is  a perfect  level- 
ness of  surface  ; the  top  of  the  water  is  smooth. 

55.  An  uniform  levelness  of  surface  takes  place  in 
every  connected  mass  of  water,  whatever  be  its  magnitude 
or  its  shape.  This  forms  the  third  leading  feature  in  the 
laws  of  water,  and  is  the  cause  of  many  of  the  phenomena 
m nature. 

56.  One  of  the  most  familiar  exam- 
ples of  the  equal  height  and  levelness 
of  surface  of  water  is  that  observable 
in  a common  teapot.  In  the  represen- 
tation of  a teapot,  Figure  10,  the  sur- 
face of  the  liquid  in  the  pot  is  seen  to 
be  at  A,  and  also  at  the  very  same 
height  at  B in  the  spout.  A straight 
dotted  line  is  drawn  from  one  to  the 
other,  to  show  that  both  surfaces  are 
of  the  same  level.  It  is  customary  to  say  that  the  small 


Fig.  111. 


39.  What  is  the  third  law  of  water  and  its  result  ? 
40  Explain  the  diagrams,  Figs.  10  and  11. 


24 


HYDROSTATICS. 


column  of  water  in  the  spout  balances  the  large  mass  of 
water  in  the  pot;  but,  in  reality,  there  is  no  balancing  in 
the  case.  The  water  necessarily  possesses  the  same  sur- 
face level  in  all  its  parts  ; one  portion  cannot  stand  higher 
than  another ; all  portions,  great  and  small,  are  only  dis- 
tributed parts  of  a single  mass. 

57.  Figure  11  presents  a similar 
example  of  the  same  phenomenon. 
V.  is  a vessel  filled  with  water  to' the 
height  of  A.  T is  a tube  proceeding 
first  downward  and  then  upward  from 
the  bottom  of  the  vessel.  In  this  tube, 
accordingly,  the  water  stands  at  the 
same  height  or  level  at  B as  it  does 
at  A.  There  is  nothing  surprising 
in  this,  because  it  is  only  the  same 
piece  of  water  throughout. 

58.  Figure  12  represents  a vessel  formed  of  six  differ- 
ent compartments,  but  all  communicating  with  eac'h  other, 
and  containing  a body  of  water.  As  in  the  preceding 
instance,  the  water  stands  at  a uniform  level  throughout, 
marked  from  A to  B,  notwithstanding  the  difference  of 
shape  of  the  compartments.  Thus,  it  is  of  no  consequence 
how  we  bend  or  twist  the  vessel  into  various  shapes,  for 
in  every  connected  mass  of  water  there  must  necessarily 
be  but  one  uniform  level. 


Fig.  12. 

59.  The  tendency  which  water  has  to  stand  at  the  same 
surface  level  in  all  parts  of  its  mass,  is  usually  referred  to 
by  the  phrase  “ water  finding  its  level.” 


41.  What  does  Fig.  12  illustrate  ? 


LEVELS. 


60.  It  is  this  inherent  tendency  in  water  to  find  its  level 
that  produces  the  various  phenomena  of  the  trickling  down 
of  rain  and  moisture  into  the  ground,  the  flowing  of  all 
kinds  of  streams,  from  the  small  brook  to  the  mighty  river, 
and  the  shooting  of  rapids  and  cataracts  over  precipices. 
In  each  case,  the  water,  in  obedience  to  the  natural  law 
or  tendency  which  governs  it,  is  only  trying  to  find  its 
level.  In  pursuit  of  this  object,  the  water,  by  the  rubbing 
force  which  it  exercises,  wears  down  all  the  solid  objects 
which  pres  nt  an  obstacle  to  it  in  its  course.  Thus,  the 
substances  of  which  hills  and  plains  are  composed,  are 
carried  away  by  streams  into  the  ocean — the  ground  of  con- 
tinents and  islands  diminishes  in  bulk — new  land  rises  in 
the  sea:  and  so,  by  the  effects  of  a simple  natural  cause, 
great  alterations  are  produced  in  the  external  features  of 
the  globe. 

LEVELS. 

1.  There  are  two  kinds  of  levels — the  true  level  and 
the  natural  level.11’ 

62.  The  true  level  is  a perfectly  horizontal  plane,  as  for 

instance  an  even  line,  thus , or  a 

perfectly  even  surface  of  a floor. 

63.  The  natural  level  is  a surface,  every  point  of  which 
is  at  the  same  distance  from  the  centre  of  the  earth.  The 
surface  level  of  water  is  always  the  natural  level. 

64.  The  character  of  a natural  level  is  understood  by  a 
reference  to  the  spherical  shape  of  the  earth  and  the  pres- 
sure of  gravitation.  The  globe  is  a ball,  and  any  piece 
of  water  which  lies  upon  it,  lies  in  the  form  of  a plaster 
round  the  ball.  Water,  therefore,  cannot  possibly  have  a 
true  surface  level ; its  level  partakes  of  the  sphericity  of 
the  ball.  Every  piece  of  water,  in  a state  of  entire  or  par- 
tial repose,  is  in  this  manner  convex  in  its  surface. 

65.  The  degree  of  convexity  of  the  earth  is,  as  nearly 

* In  mathematics,  the  term  apparent  level  is  used  instead  of  true 
level,  and  the  term  dead  level  instead  of  natural  level. 


42.  What  natural  phenomena  are  thus  explained? 

43.  How  many  kinds  of  levels  are  named  ? 

44.  Is  the  natural  level  of  water  convex,  and  why  T 


26 


HYDROSTATICS. 


as  it  can  be  stated  in  figures,  7 inches  and  9-10ths  of  an 
inch,  or  nearly  8 inches  in  each  mile.  The  convexity, 
however,  is  somewhat  less  toward  the  north  and  south 
poles,  because  the  earth  is  a spheroid,  or  a sphere  flattened 
at  the  ends. 

66.  Figure  13  represents  a segment  of  the  earth’s  sur- 

p face,  with  the  appear- 

ance of  a true  and 
natural  level  marked 
upon  it.  The  curve 
ES  is  the  earth’s  sur- 
face. PC  is  a per- 
pendicular line  point- 
ing to  the  centre  of 
the  earth.  At  right 
angles  from  this  line, 
a line  TL  is  drawn, 
representing  the  true 
level.  Supposing  that 
the  line  TL  is  a mile  in  length,  if  we  draw  a line  from  L 
to  the  centre  at  C,  it  will  cut  across  the  surface  of  the  earth 
at  a point  a mile  distant  from  the  line  at  T.  which  point 
will  be  7 inches  and  9-IOths  depressed  below  the  part  at  L. 

67.  The  convexity  of  the  earth’s  surface  is  not  observ- 
able in  small  quantities  of  water.  The  surface  of  a glass 
of  water  is  not  a true  level,  but  the  degree  of  convexity  is 
so  small  that  it  cannot  be  practically  estimated  or  measured. 
It  is  only  when  a sheet  of  water  is  stretched  out  to  an  ex- 
tent of  several  miles,  that  the  convexity  becomes  conspi- 
cuous. It  is  very  perceptible  on  the  ocean  when  a ship 
is  seen  approaching  on  the  horizon  ; first  the  mast  and 
sails  of  the  ship  are  seen,  and  lastly  the  hull.  In  order 
to  catch  the  first  glimpse  of  vessels  at  sea,  the  point  of  out- 
look for  them  is  placed  high  above  the  water.  By  this 
means,  the  person  who  looks  is  able  to  see  over  a part  of 
the  convexity,  and  give  information  of  the  approach  of 
vessels  to  those  placed  below. 


45.  What  is  the  degree  of  convexity  of  the  globe  ? 

46.  Explain  the  diagram. 

4 t.  How  is  the  spherical  level  of  the  ocean  seen  ? 


LEVELS THE  THEODOLITE. 


68.  The  convexity  of  the  land  is  not  so  conspicuous,  in 
consequence  of  the  many  risings  and  failings  in  the  sur- 
face. It  is  only  in  some  extensive  alluvial  plains  in 
different  parts  of  the  world  that  the  convexity  can  be  per- 
ceived, in  the  same  manner  as  at  sea. 

69.  In  forming  roads,  railways,  and  canals,  it  is  neces- 
sary to  make  allowance  for  the  convexity  of  the  earth’s 
surface.  The  first  thing  done  in  such  cases  is  to  survey 
the  land  by  means  of  an  instrument  called  a theodolite. 
One  of  the  varieties  of  the  theodolite  is  a small  telescope  fixed 
on  a stand,  and  must,  when  looked  through,  be  placed  per- 
fectly horizontal,  or  in  a true  level.  To  find  a true  level, 
an  instrument  is  fixed  below  it,  called  a spirit  level,  and 
by  that  it  is  regulated. 

70.  A spirit  level  is  in  universal  request  in  works  of 
art  requiring  levelness  of  foundation  or  surface.  It  con- 

a b c sists  of  a cylindrical  glass  tube, 

■-  quantity  of  spirits  of  wine  suffi- 

14  cient  to  fill  it,  except  a small  part, 

in  which  the  air  is  left.  The  tube 
being  completely  closed  or  sealed,  the  small  vacancy  where 
the  air  is  le/t  shows  an  air-bubble  at  whatever  part  of  the 
tube  is  uppermost.  The  tube  being  set  in  a small  wooden 
case  with  a level  bottom,  this  case  is  laid  upon  the  block 
of  stone,  wood,  or  other  object  to  be  levelled,  and  when 
the  air-bubble  is  seen  to  rest  in  the  middle  of  the  upper 
side,  it  signifies  that  the  object  on  which  the  instrument 
lies  is  a true  level.  In  the  accompanying  figure,  the  air- 
bubble  is  seen  at  the  middle  at  b ; the  slightest  unevenness 
would  cause  the  bubble  to  proceed  to  a at  one  end,  or  c at 
the  other. 

71.  A true  level  being  found  for  the  theodolite,  the  sur- 
veyor looks  through  the  glass  or  telescope  towards  a pole, 
the  lower  end  of  which  rests  on  the  ground,  and  is  held 
in  a perpendicular  position  by  a man  at  (we  shall  suppose) 
the  distance  of  a mile,  previously  measured.  The  pole 
having  figures  marked  upon  it,  a certain  figure  on  a level 


48.  By  what  instrument  is  the  convexity  of  the  land  measured  I 

49.  Explain  the  diagram,  and  the  use  of  the  spirit  level. 


28 


HYDROSTATICS. 


with  the  eye  is  ascertained  ; 7 inches  and  9-10ths  are  then 
reckoned  down  the  pole  from  the  figure,  and  at  that  depth 
we  have  the  natural  level  from  which  the  surveyor  makes 
his  subsequent  calculations.  If  a road  were  to  be  made 
on  the  plan  of  preserving  a true  level,  it  would  proceed 
in  its  course  at  a tangent  from  the  earth’s  convexity  like 
the  line  TL  in  Figure  13,  and,  consequently,  would  reach 
a point  above  that  to  which  it  was  destined  to  go.  It 
would  be  impossible  to  make  the  water  in  a canal  pursue 
a true  level ; in  the  attempt  to  do  so,  the  water  would  not 
remain  at  rest  in  the  channel  prepared  for  it,  but  would 
rush  towards  the  lower  end. 

72.  As  most  countries  are  less  or  more  irregular  in  sur- 
face, canals  are  usually  constructed  with  different  levels, 
so  much  of  the  length  being  on  one  1 vel,  and  so  much  on 
another,  as  the  case  may  be.  At  every  change  of  level 
there  is  a lock,  or  portion  enclosed  with  gateways,  to  keep 
the  water  at  the  proper  level,  and  to  allow  the  passage  of 
vessels.  The  locks  of  a canal,  therefore,  are  like  steps  of 
a stair,  one  at  a greater  height  than  another,  and  by  their 
means  vessels  may  be  made  to  proceed  up  or  down  hill. 

HYDROSTATICS  CONTINUElf. 

SPECIFIC  GRAVITY. 

73.  The  more  dense  in  substance  that  a body  is,  it  is 
the  more  heavy  or  weighty,  because  it  contains  the  more 
particles  to  be  operated  upon  by  attraction  of  gravitation. 
In  reference  to  the  density  of  bodies,  the  term  specific 
gravity  is  employed  to  denote  the  comparison  which  is 
made.  Thus,  the  weight  of  a lump  of  lead  is  greater  than 
an  equal  bulk  of  cork  ; therefore  its  specific  gravity  is 
greater;  and  so  on  with  all  other  substances,  when  com- 
pared together.  For  the  sake  of  convenience,  pure  distilled 
water,  at  a temperature  of  62  degrees,  has  been  established 
as  a standard  by  which  to  compare  the  specific  gravity  or 


50.  Describe  the  use  of  a theodolite  in  canalling,  &c. 

51.  By  what  means  is  the  level  changed  in  canals  1 

52.  What  results  are  thus  obtained  l 


SPECIFIC  GRAVITY. 


2? 


relative  weight  of  solid  and  liquid  bodies.  Every  such 
body  is  said  to  be  of  either  a greater  or  less  specific  gravity 
than  water,  bulk  for  bulk.* 

74.  We  have  an  example  of  a difference  in  the  specific 
gravities  of  liquids,  in  mercury,  water,  oil,  and  spirits. 
Mercury  is  considerably  more  dense  or  heavy  than  any  of 
the  others  ; the  next  in  density  is  water,  then  oil,  and  lastly 
spirits.  If  we  put  a quantity  of  each  of  these  liquids  into 
a glass  vessel,  one  after  the  other,  in  the  order  here  men- 
tioned, we  shall  observe  that  all  keep  their  respective 
places,  without  intermixture,  the  heaviest  at  the  bottom 
and  the  lightest  at  the  top.  Should  they  even  be  jumbled 
together  in  the  vessel,  it  will  be  noticed  that  they  in  time 
rectify  the  disturbance,  each  assuming  its  own  position. 

75.  Sea  or  salt  water,  in  consequence  of  being  loaded 
with  foreign  matter,  is  of  greater  density  or  specific  gravity 
than  pure  fresh  water  of  the  same  temperature.  If  we 
therefore  pour  a quantity  of  salt  water  into  a glass  vessel, 
and  then  gently  place  some  fresh  water  above  it,  we  shall 
observe  the  same  phenomenon,  of  each  kind  of  liquid  re- 

t-iining  its  position,  the  heaviest  to  the  bottom,  and 
the  lightest  to  the  top.  After  being  jumbled  to- 
gether, the  two  liquids  will,  as  far  as  possible,  re- 
turn to  their  former  relative  position. 

76.  If  we  fill  a bottle  with  water,  and  dip  it 
with  the  open  mouth  downwards  into  a jar  or 
barrel  of  spirits,  the  water,  in  virtue  of  its  density, 
will  be  emptied  and  sink  into  the  spirits,  and  the 
spirits  will  immediately  rush  up  into  the  empty 
bottle  and  supply  the  place  of  the  water. 

77.  The  force  which  liquids  exert  in  opposing 
each  other  in  a state  of  equilibrium,  corresponds 
to  their  specific  gravities  ; in  other  words,  a small 
quantity  of  a heavy  liquid  will  balance  a much 

* See  paragraph  127  to  131,  Laws  of  Matter  and  Motion. 


53.  What  of  specific  gravity,  and  what  is  the  standard  ? 

54.  What  variety  in  specific  giavity  may  be  shown7 

55.  What  of  salt  and  fresh  water,  frnngeib  erii  nislq/.S  Sc. 
•SSibWhffBBiJJsdnmemiivir^ltetSI-jjqa  oviishn  aril  onu./i  .86 


30 


HYDROSTATICS. 


greater  quantity  of  a lighter  liquid.  For  example,  take 
a bent  glass  tube,  as  in  Figure  15,  and  pour  as  much 
water  into  it  as  will  extend  from  the  bottom  at  E to  A. 
This  quantity  of  water  will  be  balanced  or  kept  to  its  sum- 
mit level  at  A by  a quantity  of  mercury  measuring  from 
E to  B,  or  by  a quantity  of  oil  from  E to  C,  or  by  a quan- 
tity of  spirits  from  E to  D.  Each  of  these  experiments 
may  be  performed  one  after  the  other.  The  pressure  of 
liquids  being  as  the  vertical  height,  and  not  as  breadth,  it 
would  make  no  difference  in  the  result  of  the  experiments, 
if  the  limb  of  the  tube  for  the  mercury,  oil,  or  spirits,  were 
increased  to  a foot,  a mile,  or  any  other  diameter. 

78.  Water,  at  its  ordinary  temperature  of  62  degrees, 
has  a specific  gravity  of  1000  ounces  to  the  cubit  foot. 
Platinum  is  22$  times  heavier,  or  22!  times  the  specific 
gravity  of  water ; gold  is  19!,  mercury  13!,  copper  8f , 
iron  8,  common  stone  about  2!,  and  brick  2.  Alcohol  is 
a little  more  than  8-10ths  of  the  heaviness  or  specific 
gravity  of  water,  or  0-815;  and  oil  of  almonds  is  little 
more  than  9-10ths,  or  0 913.  Atmospheric  air  at  the 
earth’s  surface  is  1-S00th  part,  or  0-00125 ; in  other 
words,  while  a cubic  foot  of  water  weighs  1000  ounces, 
a cubic  foot  of  air  weighs  one  ounce  and  a quarter. 

79.  Sea-water  generally  possesses  a specific  gravity 
of  1-035 — that  is,  to  1090  parts  of  fresh  water  there  are 
in  addition  55  parts  of  saline  substances.*  Sea-water 
being,  therefore,  thirty-five  parts  for  every  1000  of  water 
more  dense  than  fresh  water,  it  possesses  a proportionally 
greater  power  of  buoying  up  bodies.  A vessel  which 
will  carry  1000  tons  on  fresh  water,  will  thus  carry  1035 
tons  on  the  sea. 

FLUID  SUPPORT. 

80.  The  immersion  of  solid  bodies  in  liquids  developes 
some  important  principles  in  hydrostatics. 

* This  is  given  only  as  a general  rule.  The  sea  is  not  uniformly 
salt. 


57.  Explain  the  diagram. 

58.  Name  the  relative  specific  gravities  of  different  bodies. 


FLUID  SUPPORT. 


31 


81.  Any  body  of  greater  specific  gravity  than  water, 
bulk  for  bulk,  will  sink  on  being  thrown  into  water;  but 
a body  will  float  if  its  specific  gravity  be  less  than  that  of 
water. 

82.  The  mode  of  stating  the  law  in  reference  to  the 
immersion  and  floating  of  solid  bodies  in  any  kind  of 
fluids,  is  as  follows  : — 

83.  First. — Any  solid  body  immersed  in  a fluid  dis- 
places exactly  its  own  bulk  of  fluid,  and  the  force  with 
which  the  body  is  buoyed  up  is  pqual  to  the  weight  of  the 
fluid  which  is  displaced  ; therefore,  the  body  will  sink  or 
swim,  according  as  its  own  weight  is  greater  or  less  than 
the  bulk  of  displaced  fluid.  This  refers  to  bodies  of  less 
density  than  water. 

84.  Seccnd. — Any  solid  body  of  a greater  density  than 
water,  when  wholly  immersed  in  that  fluid,  loses  exactly 
as  much  of  its  weight  as  the  weight  of  an  equal  bulk  of 
the  water — that  is,  of  the  water  which  it  displaces. 

85.  It  is  of  great  importance  that  these  propositions 
should  be  fully  comprehended,  for  they  explain  innumerable 
phenomena  in  nature,  in  reference  to  the  floating  or  swim- 
ming of  bodies  in  water  or  in  the  atmosphere. 

86.  Water,  as  has  been  explained,  consists  of  innume- 
rable small  particles,  pressing  in  all  directions,  or  upwards 
as  well  as  downwards.  Let  us  fix  our  attention  on  a sup- 
posed single  particle  in  the  mass ; while  the  liquid  is  in  a 
condition  of  repose,  we  may  imagine  the  particle  to  be  sus- 
tained between  contending  forces — the  force  of  a column 

of  particles  above,  and  the  equally  strong 
force  of  particles  beneath,  pushing  to  get 
upward  or  away  from  this  column. 

87.  Let  us  now  substitute  any  solid 
object  for  the  supposed  particle  ; for  ex- 
ample, the  quadrangular  object  AB  re- 
Fig.  16.  presented  in  a vessel  of  water,  Figu  re  1 ;. 

This  object,  supposed  to  be  of  the  same  density  as  water. 


59.  Upon  what  does  the  floating  of  bodies  depend  ? 

60.  What  of  bodies  less  dense  than  water  ? 

61.  And  what  of  those  of  greater  density  than  water? 

62.  Do  these  laws  apply  to  all  other  fluids  ? 


HYDROSTATICS, 


>'T 

which  w e see  is  sunk  in  a buoyant  condition  in  the  water, 
has  displaced  a mass  of  particles,  all  of  which  were  ope- 
rated upon  in  the  manner  of  the  supposed  single  particle. 
This  object,  then,  by  taking  the  place  of  the  mass  of  par- 
ticles, has  become  subject  to  the  same  contending  forces, 
a id  is  consequently  floated  or  sustained  to  the  same  ex- 
tent as  they  were. 

88.  If  we  suppose  that  the  weight  of  the  object  is  two 
pounds,  liquid  to  the  amount  of  two  pounds  is  displaced, 
and  the  object  is  pressed  upwards  with  the  force  of  two 
pounds.  Or,  to  vary  the  example,  suppose  that  only  the 
lower  half  beneath  the  line  C is  the  solid  object,  and  that 
the  space  occupied  by  the  upper  half  is  water,  the  object 
is  still  pressed  upwards  with  a force  of  two  pounds;  but 
being  one  pound  weight  in  itself,  and  having  a pound  of 
water  above  it,  it  remains  suspended  in  equilibrium. 

89.  These  examples  refer  to  bodies  which  are  of  the 
same  density  or  weight  as  water,  bulk  for  bulk : we  shall 
now  take  an  example  of  a body  specifically  lighter  than 
water,  by  which  it  will  be  observed  that  the  buoyancy  is 
governed  by  the  same  principle. 

90.  Figure  17  represents  a solid  ob- 
ject A B half  immersed  in  a vessel  of 
water.  In  this,  as  in  all  cases  in  which 
there  is  a portion  of  the  object  above  the 
water,  the  weight  of  that  portion  is  borne 
by,  and  therefore  conveyed  to,  the  por- 
tion which  is  immersed.  Thus,  in  the 
example  before  us,  the  portion  B,  though  less  than  a 
pound  weight  in  itself,  by  supporting  A,  becomes,  we 
shall  say,  a pound,  and  displaces  a pound  of  water;  it  is 
therefore  buoyed  up  with  the  corresponding  force  of  a 
pound. 

91.  Whether  a body  be  large  or  small  in  bulk,  in  pro- 
portion to  its  weight,  its  displacement  of  water  depends 
exclusively  on  its  weight,  so  long  as  it  is  not  heavier  than 
water.  A vessel  of  cork,  wood,  or  any  substance  lighter 
than  water,  weighing  a thousand  tons,  displaces  exactly 


63.  'Explain  the  diagram  and  its  purpose. 

64.  Explain  the  diagram  and  its  principle 


FLUID  SUPPORT. 


33 


the  same  weight  of  water,  or  is  buoyed  up  with  the  same 
degree  of  force. 

92.  From  these  circumstances,  it  appears  that  the  en- 
tire weight  of  any  floating  body  may  be  calculated  by 
measuring  the  quantity  of  water  which  it  displaces. 

93.  On  immersing  a stone  or  any  other  solid  object  in 
water,  it  is  found  to  be  buoyed  up  in  proportion  as  its 
specific  gravity  is  less  than  that  of  water.  If  its  specific 
gravity  be  greatef  than  water,  it  will  sink  to  the  bottom, 
and  if  less,  it  will  swim.  As  the  water  of  the  ocean  be- 
comes of  greater  specific  gravity  the  greater  the  depth,  it 
may  happen  that  an  object,  which  sinks  at  the  top  of  the 
water,  will  remain  suspended  in  equilibrium  when  it 
descends  to  a point  at  which  the  specific  gravity  of  the 
water  is  equal  to  its  own. 

94.  Whatever  be  the  weight  of  any  solid  object  when 
weighed  in  air,  its  apparent  weight  is  lessened  when 
weighed  in  water.  Thus  a stone  may  be  moved  with 
comparative  ease  in  water,  which  cannot  be  lifted  without 
considerable  difficulty  on  land.  The  apparent  diminution 
of  weight  in  these  cases  is  caused  by  the  support  afforded 
by  the  liquid.  Attraction  of  gravitation,  which  is  the 
cause  of  what  we  call  weight,  is  counteracted  more  in 
water  than  in  air,  because  the  water  has  a tendency  to 
buoy  up  the  object.  The  weight  of  any  object  in  water 
is  thereby  lessened  to  the  extent  of  the  weight  of  a bulk 
of  liquid  equal  to  the  size  of  the  object.  If  the  object 
displace  a pound  of  water,  it  will  weigh  a pound  lighter 
in  water  than  in  air. 

95.  The  circumstance  of  any  solid  object  displacing  its 
own  bulk  of  liquid,  and  losing  exactly  as  much  of  its 
weight  as  the  weight  of  that  bulk  of  liquid  which  it  dis- 
places, has  led  to  the  use  of  the  hydrostatic  or  water  balance 
for  ascertaining  the  intrinsic  value  of  gold  and  other  precious 
metals.  For  example,  by  knowing  in  the  first  place  how 
much  water  a pound  of  pure  gold  displaces,  and  then 
weighing  in  water,  as  in  Figure  18,  an  object  said  to  be 
a pound  of  gold,  we  should  observe  whether  it  displaced 


65-  How  may  the  weight  ot  any  floating  body  be  measured  ? 
66.  What  difference  between  water  and  air,  and  why? 


HYDROSTATICS. 


34 

the  proper  quantity  of  water;  if  it  displaced  more  than 
was  proper,  then  we  should  be  certain  that  it  contained 

alloy  or  some  inferior  sub- 
stance, being  too  bulky  for 
a pound  of  gold.  Such 
weights  are  used  by  gold- 
smiths.* 

96.  Thus,  if  a piece  of 
gold  weigh  19^  ounces 
in  air,  it  wrould  weigh 
only  18s  ounces  in  water ; 
the  ounce  of  weight  thus 
counteracted  being  just  the  weight  of  the  water  that  the 
gold  displaces.  Therefore  the  weight  of  the  gold  would 
be  to  that  of  the  water  as  19s  ounces  to  1 ounce;  that  is, 
the  specific  gravity  of  gold  is  19^,  if  water  is  taken  for  the 
standard. 

97.  We  may  cause  an  object,  such  as  a light  hollow 
ball,  or  bladder,  to  displace  much  more  water  than  what 
is  equal  to  its  own  weight ; but  in  doing  so,  we  must  press 
the  ball  into  the  water,  and  that  degree  of  pressure  com- 
pensates the  deficiency  of  weight  in  the  ball.  Thus, 
extraneous  pressure  on  a floating  body,  and  weight  in  the 
body  itself,  are  the  same  thing  as  respects  buoyancy. 

98.  The  human  body  in  a state  of  health,  with  the 
lungs  full  of  air,  is  specifically  lighter  than  water,  and 
more  so  in  the  sea  than  in  fresh-water.  Persons,  there- 
fore, on  going  or  falling  into  water,  cannot  possibly  sink, 
unless  they  struggle  so  as  to  prevent  the  liquid  from 
buoying  them  up.  The  body  will  float  with  a bulk  of 
about  half  (he  head  above  the  surface  ; and  thus  a person 
who  cannot  swim  may  live  and  breathe,  until  chilled  or 
otherwise  paralyzed,  by  simply  stretching  himself  on  his 
back,  and  with  his  face  above  the  water.  By  throwing 
the  arms  out  of  the  water,  the  body  does  not  displace  so 

* See  paragraph  132,  Laws  of  Matter  and  Motion. 


Fig.  18. 


67.  Explain  the  nature  and  use  of  the  hydrostatic  balance. 

68.  What  of  gold  as  compared  to  water  ? 

69.  How  is  buoyancy  affected  by  ex  ra:  eous  pressure  l 


FLUID  SUPPORT. 


35 


much  liquid;  its  weight  is  increased,  and  it  naturally 
sinks.  Ignorance  of  these  facts  in  hydrostatics,  and  want 
of  resolution,  cause  many  deaths  by  drowning. 

99.  There  are  various  kinds  of  apparatus  for  prevent- 
ing drowning,  called  life-preservers.  The  most  common 
are  those  which  consist  of  pieces  of  cork  or  other  very 
light  material  attached  to  the  upper  part  of  the  body. 
But  air-tight  bags  are  preferable,  as  they  may  be  said 
scarcely  to  encumber  the  body  when  empty,  and,  as  dan- 
ger approaches,  they  can  be  inflated  with  ease  by  being 
blown  into.  Life-boats  have  large  quantities  of  cork  in 
their  structure,  and  also  air-tight  vessels  made  of  thin 
metallic  plates ; so  that,  even  when  the  boat  is  filled  with 
water,  a considerable  portion  of  it  still  floats  above  the 
g.  nera!  surface.  The  bodies  of  some  animals,  as  sea-fowl, 
and  many  other  species  of  birds,  are  considerably  lighter 
than  water.  The  feathers  with  which  they  are  covered 
add  very  much  to  their  buoyancy.  Quadrupeds  swim 
much  easier  than  men.  because  the  natural  motion  of  their 
legs  in  walking  or  running  is  that  which  best  fits  them  for 
swimming.  Fishes  are  enabled  to  change  their  specific 
gravity  by  means  of  an  air-bag  with  which  they  are  pro- 
vided. When  the  air-bag  is  distended,  thpy  rise  to  the 
surface ; when  it  is  contracted,  they  descend  to  the  bot- 
tom.* 

100.  The  buoyant  property  of  liquids  is  independent 
of  their  depth  or  expanse,  for  if  there  be  only  enough  of 

* The  bodies  of  most  fishes  are  nearly  of  the  specific  gravily  of 
water,  and,  therefore,  if  living  in  it  without  making  exertion, 
they  neiiher  sink  nor  swim.  When  ihis  subject  was  less  understood, 
many  persons  believed  that  fishes  had  no  weight  in  water ; and  it  is 
related  as  a joke  at  the  expense  of  the  philosophers,  that  a king  having 
once  proposed  as  a task  to  his  men  of  science  to  explain  this  extraor- 
dinary fact,  many  profound  disquisitions  came  forth,  but  not  one  of 
the  competitors  thought  of  trying  what  really  was  the  fact.  At  last, 
a simple  man  [who  doubted  the  fact]  balanced  a vessel  of  water  in 
scales,  and  on  putting  a fish  into  it,  showed  a scale  preponderating, 
just  as  much  as  if  the  fish  had  been  weighed  alone. — Arnott’ s Ele- 
ments of  Physics. 


70.  What  useful  lesson  is  given  here  ? 

71.  What  of  life-preservers  ? 

72.  What  animal  peculiarities  are  named  ? 


HYDROSTATIC^. 


86 

water  to  surround  an  object  plunged  into  it,  the  object 
will  float  as  effectually  as  if  it  had  been  immersed  in  a 
large  mass  of  water.  Thus,  a few  pounds  of  water  may 
float  an  object  which  is  a ton  in  weight.  We  account  for 
these  phenomena,  by  the  law  of  pressure  in  liquids  being 
as  vertical  height,  not  as  width  of  column,  and  by  a body 
being  buoyed  up  with  a force  exactly  in  proportion  to  the 
weight  of  water  which  it  displaces. 

101.  These  important  truths  in  hydrostatics  teach  the 
practical  lesson  that  if  canals  be  made  only  as  deep  or 
wide  as  will  afford  water  to  surround  the  vessels  placed 
upon  them,  they  will  be  sufficiently  large  for  all  purposes 
of  buoyancy  and  navigation.  A ship  floats  no  better  on 
the  face  of  a sheet  of  water  miles  in  width,  than  it  would  do 
on  a mill-pond,  provided  there  be  enough  of  water  in  the 
pond  to  keep  it  off  the  bottom. 

102.  Every  solid  body  possesses  a centre  of  gravity, 
which  is  the  point  upon  or  about  which  the  body  balances 
itself,  and  remains  in  a state  of  rest,  or  equilibrium,  in  any 
position. 

103.  The  equilibrium  of  floating  bodies  is  regulated  in 
the  same  manner.  The  floating  body  has  a centre  of 
gravity,  about  which  the  whole  mass  will  balance  itself  in 
the  liquid ; the  heaviest  side  will  sink  lowest,  and  the 
more  light  will  be  uppermost. 

104.  In  reference  to  floating  bodies,  there  is  a point 
called  the  centre  of  buoyancy ; this  is  the  centre  of  gravity 
of  the  liquid  which  is  displaced.  If  the  floating  body  be 
of  the  same  specific  gravity  as  water,  the  centre  of  buoy- 
ancy will  be  at  the  same  point  in  the  floating  body  as  it 
would  have  been  in  the  water;  but  there  is  seldom  this 
uniformity,  at  least  not  in  vessels  used  for  purposes  of 
navigation.  It  is  necessary  that  all  such  vessels  should 
be  of  a less  specific  gravity  than  water,  in  order  that  a 
part  of  their  weight  may  be  composed  of  cargo,  stores, 
passengers,  &c.,  and  that  they  may  be  sufficiently  buoyant. 

105.  Besides  the  centre  of  gravity  and  centre  of  buoy- 


73.  By  what  law  is  the  buoyancy  of  water  calculated? 

74.  What  practical  hints  are  thus  given  ? 


FLUID  SUPPORT. 


37 


ancy  of  a floating  body,  there  is  another  important  point 
called  the  metarentre,  a word  signifying  beyond  the  centre 
This  metacentre  is  a point  in  the  axis  of  a floating  body , 
the  axis  being  a vertical  line  through  the  centre  of  gravity 
of  the  mass  when  it  is  at  rest.  In  the  case  of  a body 
floating  at  rest  or  perfectly  stable,  an  ideal  line  uniting  the 

centre,  of  gravity 
and  buoyancy  is 
in  a vertical  posi- 
tion. as  from  B to 
G,  Figure  19,  and 
is  called  the  line 
of  support.  W W 
is  the  water  line. 
If  the  body  is  now 
inclined  a little  to 
one  side,  as  in  Figure  20.  the  direction  of  this  line  is  no 
longer  vertical,  but  slanting,  as  a line  uniting  B and  G, 
(not  shown  in  the  cut.)  If  a line  be  supposed  to  pass 
upwards  in  a vertical  direction  from  the  centre  of  buoy- 
ancy B,  it  will  meet  the  axis  on  a point  marked  M,  which 
is  the  metacentre.  Should  the  body  sway  in  an  opposite 
direction  to  the  same  extent,  the  point  M will  still  be  the 
metacentre.  For  different  small  inclinations  from  the 
position  of  equilibrium,  the  position  of  the  metacentre  is 
nearly  the  same ; but  for  greater  deviations,  its  position 
varies  considerably. 

106.  We  have  now  to  explain  the  practical  use  of  a 
knowledge  of  these  facts.  When  the  metacentre  happens 
to  lie  above  the  centre  of  gravity,  as  in  the  figure,  the 
force  of  buoyancy  acting  upwards  in  the  direction  of  the 
line  B M,  makes  the  body  turn  round  its  centre  of  gravity 
G,  till  it  arrive  at  its  position  of  rest,  as  in  figure  19,  after 
performing  a few  oscillations.  But  if  the  metacentre 
happen  to  lie  below  the  centre  of  gravity,  the  buoyant 
force  would  turn  the  body  in  an  opposite  direction,  and  make 


75  Define  the  centre  of  gravity  and  of  nuoyancy. 

76.  What  of  vessels  used  in  navigation  ? 

77.  Define  the  meiaeentre  and  exp'ain  the  diagrams. 

78.  Of  what  practical  use  is  this  metacentre  ? 


38 


HYDROSTATICS. 


it  depart  still  farther  from  its  position  of  rest,  till  it  would 
be  upset. 

107.  The  discovery  of  the  centre  of  buoyancy  and  me- 
tacentre in  any  floating  body,  is  a matter  of  mathematical 
investigation  ; the  explanations  here  given,  however,  will 
show  the  nature  of  the  calculations  required  in  reference 
to  the  laws  which  secure  the  stability  of  floating  bodies. 

108.  Heavy  materials,  called  ballast,  are  usually  placed 
in  the  bottom  of  the  holds  of  vessels,  to  insure  a low  centre 
of  gravity.  A ship  of  the  largest  capacity  and  burden, 
with  its  centre  of  gravity  properly  regulated,  rests  in  the 
water  with  a stateliness  and  stability  which  cannot  be  de- 
stroyed except  by  some  extraordinary  violence. 

HYDROMETERS. 

109.  If  a substance  be  weighed  in  two  fluids,  the 
weights  which  it  loses  in  each  are  as  the  specific  gravities 
of  those  fluids.  Thus,  a cubic  inch  of  lead  loses  g53 
grains  when  weighed  in  water,  and  only  209  grains  when 
weighed  in  rectified  spirit ; therefore,  a cubic  inch  of  rec- 
tified spirit  weighs  209  grains,  an  equal  bulk  of  water 
weighing  253;  and  so  the  specific  gravity  of  water  is 
about  a fourth  greater  than  that  of  the  spirit. 

1 10.  The  instrument  called  a hydrometer  is  constructed 
upon  this  principle.  Its  name  is  derived  from  two  Greek 
words,  signifying  measure  of  water ; but  it  is  of  course 
used  fo.-  ascertaining  the  density  of  all  kinds  of  liquids. 
There  are  various  kinds  of  hydrometers.  One  of  them 
consists  of  a glass  or  copper  ball  with  a stem,  on  which  is 
marked  a scale  of  equal  parts  or  degrees.  When  im- 
mersed in  any  fluid,  the  stem  sinks  to  a certain  depth, 
which  is  indicated  by  the  graduated  scale.  The  length 
to  which  it  sinks  in  the  standard  of  comparison  being 
known,  we  can  thus  easily  ascertain  how  much  it  is  spe- 
cifically heavier  or  lighter  than  the  fluid. 

111.  Much  in  the  same  manner  is  constructed  another 
hydrometer  of  great  delicacy  and  exactness.  It  consists 


79.  What  difference  between  weight  in  waier  and  spirit  ? 

80.  How  is  the  simplest  form  of  hydrometer  made  ? 


HYDROMETERS. 


39 


of  a ball  of  glass  about  three  inches  diameter,  with  another 
joined  to  it,  and  opening  into  it,  of  one  inch  diameter,  6c, 
Figure  21,  and  a brass  neck  d,  into  which  is  screwed  a 
wire  ae,  divided  into  inches  and  tenths  of  an  inch,  about 
ten  inches  long  and  one-fortieth  of  an  inch  in  diameter. 
The  who.e  weight  of  the  instrument  is  4000  grains  when 
loaded  with  small  weights,  such  as  shot,  in 
the  lower  ball  c.  When  plunged  into  water 
in  the  jar,  this  instrument  is  found  to  sink 
an  inch,  if  a single  grain  be  laid  upon  the  top 
a ; hence  a tenth  of  a grain  sinks  it  a tenth 
of  an  inch.  So  great  is  the  delicacy  ol  this 
hydrometer,  that  the  difference  in  specific 
gravity  of  one  part  in  40,009  can  be  de- 
tected. Its  total  weight  of  4000  grains  is 
convenient  for  comparing  water;  but  the 
quantity  of  shot  in  the  lower  ball  can  be 
varied,  so  as  to  adapt  the  instrument  to 
measure  the  specific  gravities  of  fluids  light- 
er or  heavier  than  the  standard  of  compari- 
son. 

112.  There  is  another  very  simple  hydrometer,  which 
consists  of  a number  of  glass  beads  of  different  weights, 
but  whose  proportions  are  known,  and  the  beads  marked 
accordingly.  These  are  dropped  into  the  fluid  under  ex- 
amination, until  one  is  found  which  neither  sinks  to  the 
bottom  nor  swims  upon  the  surface,  but  remains  at  rest 
wherever  it  is  placed  in  the  liquid ; and  this  bead  being 
numbered,  indicates  the  specific  gravity. 

1 13.  In  making  calculations  of  the  strength  and  specific 
gravity  of  spirits,  by  the  above  or  any  other  means,  atten- 
tion must  be  paid  to  the  degree  of  temperature  of  the  liquid. 
Heat  expands  the  liquor,  and  renders  it  specifically  lighter  ; 
all  spirits  are  therefore  more  bulky,  in  proportion  to  their 
weight,  in  summer  than  in  winter,  and  also  apparently 
stronger,  not  really  so.* 

* See  paragraph  131,  Laws  or  Matter  and  Motion. 


81.  Explain  the  diagram. 

82.  How  does  temperature  vary  specific  gravity  t 


40 


HYDRAULICS. 


HYDRAULICS. 

Having  detailed  the  laws  and  properties  of  water  in  a 
state  of  rest  or  equilibrium,  we  have  now  to  mention  some 
of  the  more  important  results  of  these  laws,  and  also  the 
effects  which  are  produced  upon  liquids  by  the  application 
of  forces,  whether  natural  or  artificial. 

WATER  A MECHANICAL  AGENT. 

114.  Water,  as  already  explained  in  the  Laws  of  Mat- 
ter and  Motion,  may  be  made  a useful  agent  of  power, 
merely  by  allowing  it  to  act  with  the  force  of  its  own 
gravity,  as  in  turning  a mill;  and  in  this  manner  it  is  ex- 
tensively employed  in  ail  civilized  countries  possessing 
brooks  which  are  sufficiently  rapid  in  their  descent. 

115.  But  water  maybe  rendered  otherwise  useful  as 
an  agent  of  force  in  the  arts.  Although  subtile  in  sub- 
stance, and  eluding  the  grasp  of  those  who  d -sire  to  han- 
dle and  hold  it,  it  can,  without  alteration  of  temperature, 
be  made  to  act  as  a mechanical  ■power , as  conveniently  and 
usefully  as  if  it  were  a solid  substance,  like  iron,  stone,  or 
wood.  The  lever,  the  screw,  the  inclined  plane,  or  any 
of  the  ordinary  mechanical  powers,  are  not  more  remark- 
able as  instruments  of  force  than  water,  a single  gallon  of 
which  may  be  made  to  perform  what  cannot  be  accom- 
plished (except  at  enormous  cost  and  labour)  by  the  strong- 
est metal. 

llfj.  To  render  water  serviceable  as  an  instrument  cf 
force,  it  must  be  confined,  and  an  attempt  then  made  to 
compress  it  into  less  than  its  natural  bulk.  In  making 
this  attempt,  the  impressed  force  is  freely  communicated 
through  the  mass,  and  in  the  endeavour  to  avoid  compres- 
sion, the  liquid  will  repel  whatever  movable  object  is  pre- 
sented to  it.  The  force  with  which  water  may  be  squirted 
from  a boy’s  syringe,  gives  but  a feeble  idea  of  the  power 
of  liquids  when  subjected  in  a state  of  confinement  to  the 
impression  of  external  force. 


83.  Define  hydraulics. 

84.  What  of  water  as  a mechanical  agent  ? 

85.  How  is  water  rendered  an  instrument  of  force  ? 


HYDRAULIC  PRESS. 


41 


117.  The  mechanical  force  of  water  is  exemplified  by 
the  hydraulic  press.  This  is  an  engine  employed  by  paper- 
makers,  printers,  and  manufacturers  of  various  kinds  of 
goods,  for  the  purpose  of  giving  a high  degree  of  pressure 
or  smooth  glazed  finish  to  their  respective  articles.  It  has 
generally  superseded  the  screw  press,  on  account  of  its 
much  greater  power,  with  a less  degree  of  trouble  and  risk 
of  injury  to  the  mechanism. 


118.  Figure  22  represents  the  outline  of  a hydraulic 
press.  AB  is  the  frame,  consisting  of  four  upright  pillars 
supporting  a cross  top  of  great  strength,  and  against  which 
the  pressure  takes  place  in  an  upward  direction.  C,  the 
material  to  be  pressed,  is  forced  upward  by  D,  a round 
iron  piston.  This  piston  is  very  nicely  fitted  into  an  iron 
case  E,  which  has  a cavity  F for  receiving  the  water : the 
neck  of  the  case  grasps  the  piston  so  tightly  that  no  water 


86.  Describe  the  hydraulic  press  and  its  use. 

87.  Explain  the  diagram  and  its  principles. 


42 


HYDRAULICS. 


can  escape.  A small  pipe  G conveys  water  into  the  hollow 
cavity  from  a forcing  pump  H,  which  stands  in  a trough  of 
water  T.  All  that  part  of  the  apparatus  below  the  base  of 
the  pillars  is  sunk  out  of  sight  in  the  ground.  The  pump 
apparatus  is  here  represented  as  exceedingly  simple,  but  in 
real  machines  it  is  very  complex  and  of  great  power. 

1 19.  The  pump,  on  being  wrought,  forces  the  water  into 
the  cavity.  There  the  water,  in  endeavouring  to  escape, 
operates  upon  the  moveable  piston,  which  it  causes  slowly 
to  rise  with  its  burden.  The  pressure  thus  exerted  by  the 
liquid  almost  exceeds  belief;  unless  the  case  for  the  water 
be  of  enormous  strength,  it  will  be  rent  in  an  instant  as  if 
made  of  the  weakest  material.  When  the  weight  has  been 
raised  to  the  required  height,  a stopcock  is  turned  upon  the 
pipe,  and  the  apparatus  remains  at  rest.  The  opening  of 
the  cock  allows  the  water  to  gush  out,  and  the  weight  ac- 
cordingly sinks.* 

12d.  The  mode  of  calculating  the  power  of  the  hydraulic 
press  is  analogous  to  that  for  calculating  lever  powers. 
Thus,  the  proportion  is  estimated  between  the  small  bore  of 
the  pump  and  the  large  bore  of  the  cavity  or  barrel  for  the 
piston.  Suppose  that  the  pump  has  only  one  thousandth 
of  the  area  of  the  barrel,  and  if  a man  by  means  of  its  lever 
handle,  press  its  rod  down  with  a force  of  five  hundred 
pounds,  the  piston  of  the  barrel  will  rise  with  a force  of 
one  thousand  times  five  hundred  pounds,  or  more  than  two 
hundred  tons.  A boy  working  the  pump  by  a long  handle, 
and  taking  a sufficiency  of  time,  will  raise  a pressure  of 
thousands  of  tons. 

* The  sheets  of  the  present  treatise  are  smoothed  by  being  pressed 
between  glazed  boards  in  a hydraulic  press.  It  is  made  entirely  of  iron, 
and  wrought  by  two  forcing  pumps  ; by  these  a man  is  able  by  a quar- 
ter of  an  hour’s  labour  to  apply  from  three  to  four  hundred  tons  of 
pressure.  Each  hydraulic  press  has  a safety-valve  to  permit  the  escape 
of  water  when  a certain  pressure  has  been  attained  ; unless  there  was 
a provision  of  this  kind,  no  strength  of  metal  could  endure  the  pres- 
sure which  might  be  applied.  A good  hydraulic  press  costs  from  XI 5U 
to  £200. 


88.  How  is  its  power  calculated  ? 

S9.  How  could  the  forcing  pump  be  dispensed  with  ? 


AQUEDUCTS FOUNTAINS. 


43 


121.  In  the  hydtaulic  press,  a force-pump  is  employed 
for  the  sake  of  convenience ; the  same  end  could  be 
attained  by  a small  column  of  water  of  a great  elevation, 
on  the  principle  of  pressure  in  liquids  being  as  vertical 
height. 


AQUEDUCTS FOUNTAINS. 

122.  The  tendency  in  a liquid  to  find  its  level  has  per- 
mitted the  construction  of  apparatus,  consisting  of  pipes 
and  cisterns,  for  supplying  towns  with  water.  No  species 
of  hydraulic  machine  has  been  of  such  great  use  to  man- 
kind as  this  apparatus. 

123.  In  ancient  times,  the  fact  of  water  rising  to  an  uni- 
form level  in  every  part  of  its  volume,  was  either  not  per- 
fectly understood,  or  there  was  a deficiency  of  materials 
wherewith  to  construct  the  apparatus  required  for  carrying 
water  a great  distance. 

124.  From  whatever  cause,  towns  were  in  these  times 
supplied  with  water  by  means  of  open  canals,  either  cut  in 
the  level  ground,  or  supported  on  the  top  of  arches  built 
for  the  purpose.  These  structures,  with  their  elevated 
channels,  were  called  aqueducts.  In  Italy,  and  some  other 
countries  in  the  south  of  Europe,  the  remains  of  stupen- 
dous aqueducts,  miles  in  length,  still  exist. 

125.  By  a knowledge  of  the  laws  of  fluids,  and  by  pos- 
sessing an  abundance  of  lead  and  iron,  we  are  enabled  in 
the  present  day  to  construct  apparatus  for  supplying  towns 
with  water  in  a manner  the  most  effectual  and  simple, 
causing  a cheap  iron  or  leaden  tube,  sunk  in  the  ground, 
to  perform  the  office  of  the  most  expensive  and  magnificent 
aqueduct. 

126.  The  method  of  supplying  towns  with  water  consists 
in  leading  a pipe  of  sufficient  diameter  from  a lake,  river, 
or  fountain  of  fresh  and  pure  water,  to  the  place  where  the 
supply  is  required.  The  iron  pipes  used  for  this  purpose 
are  composed  of  a number  of  short  pieces  soldered  together, 


90.  What  of  aqueducts  and  their  value  ? 

91.  How  do  the  moderns  possess  superior  advantages  ? 


44 


HYDRAULICS. 


and  extending  to  any  length  or  in  any  direction.  From 
these  main  pipes  smaller  tubes  of  lead  are  led  into  the 


houses  requiring  the  supply  of  water ; and  by  means  of 
these  minor  tubes,  the  water  may  be  carried  to  any  point 
which  is  not  of  a higher  level  than  the  original  fountain 
affording  the  supply. 

127.  Figure  23  is  a representation  of  the  mode  of  sup- 
plying towns  with  water  in  this  convenient  manner.  A pipe 
is  observed  to  proceed  from  a lake  on  the  top  of  a hill  down 
into  a valley,  and  thence  to  supply  a house  situate  on  the 
opposite  rising  ground.  From  the  pipe  in  its  passage  across 
the  valley,  a small  tube  is  carried  to  supply  an  ornamental 
fountain  or  jet  d’eau.  The  water  spouts  from  this  jet  d’eau 
with  a force  corresponding  to  the  height  of  the  lake  above. 

128.  In  towns  not  commanding  a supply  of  water  from 
a sufficient  height,  the  water  is  forced  by  an  apparatus  of 
pumps  to  an  elevated  reservoir,  and  from  that  the  pipes  are 
laid.  When  the  water  is  impure,  or  loaded  with  muddy 
particles,  it  is  usual  to  purify  it  by  filtration  at  the  reser- 
voir; it  is  made  to  filter  or  ooze  through  a mass  of  fine 
sand,  in  which  the  particles  of  mud  are  deposited. 


92.  Explain  the  diagram  and  its  purposes. 

93.  How  is  a high  level  artificially  obtained  t 

94.  By  what  means  may  water  be  purified  1 


SPRINGS. 


45 


SPRINGS. 

129.  Springs  in  the  ground  are  natural  hydraulic  opera- 
tions, and  are  accounted  for  on  principles  connected  with 
the  laws  of  fluids. 

130.  One  kind  of  springs  is  caused  by  capillary  attraction, 
or  natural  attractive  force  by  which  liquids  rise  in  small 
tubes,  porous  substances,  or  between  flat  bodies  closely 
laid  towards  each  other.* 

131.  This  species  of  power  is  a remarkable  variety  of 
the  mutual  attraction  of  matter,  and  is  as  unaccountable  as 
the  attraction  of  gravitation,  or  the  attraction  exercised  by 
the  loadstone. 

132.  We  may  observe  the  action  of  capillary  attraction 
in  the  case  of  two  plates  of  glass  brought  almost  in  contact 

with  each  other,  and  placed 
with  their  lower  end  in  a ves- 
sel of  water.  Figure  24  re- 
presents two  glass  plates  placed 
in  this  manner  in  a vessel  of 
water.  The  plates  are  some- 
what separated  at  one  side, 
and  close  at  the  other.  We 
perceive,  therefore,  that  the  wa- 
ter has  risen  at  the  close  side, 
and  formed  a curve  in  its  upper  surface  from  A to  D,  the 
degree  of  height  of  the  liquid  being  in  proportion  to  the 
closeness  of  the  plates.  The  plates  being  more  near  each 
other  at  B than  at  C,  the  water  stands  higher  accordingly 
at  B. 

133.  The  rising  of  the  water  between  these  two  plates 
of  glass  is  precisely  analogous  to  the  rising  of  water  from 
low  situations  in  the  earth  through  small  fissures  in  rocks,  or 
through  porous  beds  of  sand  or  clay,  and  so  forming  springs. 

134.  Springs  from  capillary  attraction  are  believed  to  be 
less  common  and  of  smaller  importance  than  springs  which 

* Laws  of  Matter  and  Motion,  paragraph  41  to  45. 


95.  How  are  springs  acounted  for  ? 

96.  Explain  the  diagram. 


46 


HYDRAULICS. 


originate  from  the  obvious  cause  of  water  finding  its  level. 
The  water  which  falls  in  the  form  of  rain  sinks  rnto  the 
ground  in  high  situations,  and  finds  an  outlet  at  a lower 
level,  though  perhaps  at  a considerable  distance. 

135.  Some  springs  are  also  accounted  for  by  a reference 
to  atmospheric  action,  but  these  will  form  a subject  of  no- 
tice under  the  head  Pneumatics. 


HYDRAULICS  CONTINUED. 

FRICTION  BETWEEN  FLUIDS  AND  SOLIDS. 

136.  The  flowing  of  water  through  pipes,  or  in  natural 
channels,  is  liable  to  be  materially  afiected  by  friction.  W a- 
ter flows  smoothly,  and  with  least  retardation  from  friction, 
when  the  channel  is  perfectly  smooth  and  straight.  Every 
little  inequality  which  is  presented  to  the  liquid,  helps  to  re- 
tard it,  and  so  likewise  does  every  bend  or  angle  in  its  path. 
A smooth  leaden  pipe  will  thus  convey  more  water  than  a 
wooden  pipe  of  the  same  capacity.  Practically,  an  allowance 
is  made  in  the  magnitude  of  pipes  for  the  loss  of  speed  by 
friction.  Where  the  length  of  the  tube  is  considerable,  and 
there  are  several  bendings,  it  is  not  unusual  to  allow  a third 
of  the  capacity  for  retardation. 

137.  By  increasing  the  capacity  of  pipes,  a prodigious 
gain  is  secured  in  the  increase  of  water.  The  loss  from 
friction  on  a small  tube  of  an  inch  diameter  of  bore  is  so 
great,  that  one  of  twice  the  capacity  will  deliver  five  times 
as  much  water. 

138.  The  rate  at  which  water  flows  from  an  orifice  in  a 
reservoir,  or  containing  vessel,  is  affected  by  the  situation 
and  the  shape  of  the  orifice. 

139.  The  most  favourable  situation  for  the  orifice  is  at  the 
bottom  of  the  vessel ; but  the  velocity  of  the  emission  is  not 
in  the  ratio  of  the  height  of  the  liquid,  or  of  a perpendicu- 
lar column  of  particles,  and  the  water  presses  in  all  dtrec- 


97.  What  other  sources  of  springs  are  named  ? 

98.  How  is  the  flow  of  water  retarded  ? 

99.  What  proportion  of  gain  by  increasing  the  capacity  ? 

100.  How  is  the  flow  of  water  affected  by  the  orifice  t 


FRICTION  BETWEEN  FLUIDS  AND  SOLIDS.  47 

tions  alike  ; there  is  from  all  parts  of  the  vessel  a general 
rush  as  it  were  to  the  outlet,  thus  putting  the  whole  mass 
in  motion. 

140.  Although  the  rush  of  water  at  the  outlet  is  not  as 
the  ratio  of  the  depth,  it  depends  upon  the  depth.  Thus, 
if  a vessel  ten  feet  high  be  penetrated  at  the  side  on  a level 
with  the  bottom,  and  the  water  stand  at  two  feet  and  a half 
within,  it  will  issue  outwards  with  a certain  degree  of  ve- 
locity. If  the  height  of  the  water  be  quadrupled,  that  is,  if 
the  vessel  be  filled,  the  velocity  will  be  doubled.  In  order 
to  obtain  a threefold  velocity  a ninefold  depth  is  necessary, 
for  a fourfold  velocity  sixteen  times  the  depth  is  required, 
and  so  on.  In  fact,  in  whatever  pr  (portion  the  velocity  of 
efflux  is  increased,  the.  quantity  of  liquid  discharged  in  a 
given  time  must  be  also  increased  in  the  same  proportion  ; 
hence  the  quantity  of  water  discharged  conjointly  with  its 
degree  oi  velocity  will  be  increased  in  proportion  to  the 
pressure.  There  is  here  a striking  coincidence  between 
the  descent  of  water  and  the  relation  which  exists  between 
the  height  from  which  a body  falls,  and  the  velocity  ac- 
quired at  the  end  of  the  fall. 

141.  It  has  been  ascertained  that  water  rushes  with  most 
advantage  from  an  orifice,  when  the  orifice  is  in  the  form 
of  a short  round  tube  inserted  into  the  vessel,  and  of  a length 
equal  to  twice  its  diameter. 

142.  It  has  also  been  found,  that  if  the  pipe,  instead  of 
being  flush  or  level  with  the  bottom  of  the  reservoir,  en- 
tered into  it  to  some  distance,  it  had  the  effect  of  making 
the  flow  of  water  even  less  than  that  which  issued  through 
the  simple  hole  without  any  pipe.  The  singular  fact  of  a 
oipe  and  hole  of  the  same  diameter  discharging  different 
quantities  of  water  under  different  circumstances,  whilst 
the  head  or  pressure  remains  the  same,  must  be  accounted 
for  by  cross  or  opposing  currents  being  created  by  the  rush 
which  all  fluids  make  to  I he  orifice.  Currents  will  thus  form 
from  the  top  and  sides  of  the  containing  vessel,  and  by 


101.  How  and  what  ratio  may  the  velocity  be  varied  1 

102.  What  of  a short  tube,  and  why  the  difference  ? 

103.  What  if  the  tube  project  into  the  interior  1 


48 


HYDRAULICS. 


their  inertia  they  will  cross  each  other,  and  thus  impede 
the  descent  of  the  perpendicular  column,  causing  the  wa- 
ter which  issues  to  run  in  a screw-like  form;  this,  however, 
is  in  a great  measure  obviated  by  the  application  of  a short 
tube  from  the  aperture.  That  the  projection  of  the  tube  too 
far  into  the  interior  of  the  vessel  should  make  the  flow  less 
than  if  there  were  no  pipe  at  all,  may  be  thus  explained  : — 
The  columns  which  descend  from  near  the  outside  of  the 
vessel,  by  turning  up  again  to  reach  the  discharging  orifice, 
come  into  more  direct  opposition  to  the  motion  of  the  cen- 
tral descending  columns,  whilst  they  are  at  the  same  time 
themselves  compelled  to  turn  suddenly  in  opposition  to 
their  own  inertia  before  they  can  enter  the  pipe.  Thus, 
the  discharge  is  more  effectually  impeded  than  if  it  were 
proceeding  from  a mere  opening  in  the  bottom  of  the  vessel. 

143.  The  tube  for  the  discharge  of  water  should  not 
only  be  short  and  round,  but  also  trumpet-mouthed  or 
funnel-shaped,  both  internally  and  externally,  that  being  the 
form  which  admits  the  flow  of  liquid  with  the  least  possible 
retardation. 

144.  The  effects  of  friction  between  liquids  and  solids 
are  no  where  so  conspicuous  as  in  the  flowing  of  rivers. 
The  natural  tendency  in  the  water  to  descend  at  a certain 
speed,  is  limited  by  the  roughness  of  the  bottom,  bends  in 
the  course  of  the  stream,  and  small  projections  on  the 
banks.  From  these  causes,  the  water  in  a river  flows  with 
different  velocities  at  different  parts  in  any  vertical  section 
across  the  current.  It  flows  at  a slower  rate  of  speed  at 
and  near  the  bottom  than  at  the  surface,  and  also  slower  at 
the  sides  than  at  the  middle. 

145.  The  resistance  which  a body  moving  in  liquid 
meets  with,  when  it  comes  in  contact  with  a solid,  is  as  the 
square  of  the  velocity  of  the  moving  body  ; in  other  words, 
the  resistance  is  not  twice  but  four  times  with  a double 
rate  of  speed.  This  is  easily  explained  : — 

146.  A vessel  moving  at  the  rate  of  one  mile  per  houi 
displaces  a certain  quantity  of  water,  and  with  a certain 

104.  What  is  the  best  form  of  the  tube  ? 

105.  What  of  the  flowing  of  rivers  ? 

106.  What  relation  between  resistance  and  speed  1 


ACTION  OF  WATER  IN  RIVERS. 


49 


velocity ; if  it  move  twice  as  fast,  it  of  course  displaces 
twice  as  many  particles  in  the  same  time,  and  requires  to 
be  moved  by  twice  the  force  on  that  account;  but  it  also 
displaces  every  particle  with  a double  velocity,  and  requires 
another  doubling  of  the  power  on  this  account;  the  power 
thus  twice  doubled,  becomes  a power  of  four.  When  the 
body  is  moved  with  a speed  of  three  or  four,  a force  of  nine 
or  sixteen  is  wanted,  and  so  on.  Thus,  the  resistance  in- 
creases as  the  square  of  the  speed. 

147.  This  important  law  suggests  practical  hints  of  con- 
siderable importance.  For  instance,  in  steam  navigation, 
if  an  engine  of  fifty  horse  power  impel  a vessel  at  the  rate 
of  seven  miles  an  hour,  it  would  require  two  of  the  same 
power  to  drive  her  ten  miles  an  hour,  and  three  such  to 
drive  her  twelve  miles  an  hour.  Hence  the  enormous 
expense  of  fuel  attending  the  gaining  of  a high  degree  of 
velocity. 

ACTION  OF  WATER  IN  RIVERS. 

148.  In  cases  where  it  is  desirable  to  preserve  the  banks 
of  rivers  from  injury,  either  from  the  regular  action  of  tfie 
current  or  from  floods,  the  water  ought  to  be  allowed  a free 
open  channel  with  banks  of  a very  gradual  descent.  The 
utmost  violence  of  water  in  a stale  of  motion  may  be  ren- 
dered comparatively  harmless,  by  allowing  the  flood  or 
torrent  ,to  expend  itself  on  a sloping  or  shelving  shore. 
Inattention  to  this  simple  fact  in  hydraulics  frequently 
causes  much  destruction  to  property  on  the  banks  of  rivers. 

149.  A very  small  fixed  obstacle,  such  as  a stone  or 
pebble,  may  partially  impede  and  turn  aside  a brook  of  a 
slow  current.  The  water,  by  striking  on  a stone  at  one 
side,  is  bent  aside  to  the  opposite  bank,  a little  farther 
down ; there  it  strikes  upon  the  bank,  and  is  returned  to 
the  side  it  formerly  struck.  Thus,  proceeding  in  currents 
from  side  to  side,  the  banks  become  worn  down  at  parti- 
cular places,  and,  in  time,  a new  and  serpentine  course  is 
given  to  the  stream.  In  the  case  of  rivers  flowing  with 

107.  How  is  this  important  in  steam  navigation  1 

108.  What  of  the  action  of  water  in  rivers  ? 

109.  What  of  straight  and  winding  rivers? 


50 


HYDRAULICS. 


considerable  velocity,  impediments  of  this  kind  are  usually 
overcome,  and  the  stream  pursues  its  straight  onward 
course,  dashing  down  all  obstacles  to  its  progress.  Thus, 
rivers  are  generally  winding  in  their  course  in  flat  countries, 
and  straight  in  mountainous  regions. 

150.  It  sometimes  happens  that  the  water  at  the  surface 
of  a river  may  be  moving  in  one  direction,  while  the  water 
at  the  bottom  is  flowing  in  an  opposite  direction.  This  is 
an  exceedingly  interesting  phenomenon,  which  is  observed 
to  occur  in  certain  rivers  communicating  with  the  sea,  and 
is  caused  by  the  action  of  the  tides  and  the  difference  of 
specific  gravity  in  salt  and  fresh  water.  When  the  tide  is 
flowing  inwards,  the  salt  water  rushes  up  the  channel  of 
the  river,  but  not  at  such  a depth  as  to  stem  the  current 
of  fresh  water,  which,  being  lighter,  floats  on  the  top  of 
the  salt  water,  and  pursues  its  downward  course  to  the 
ocean.  In  those  instances  in  which  there  is  no  great  dis- 
turbance of  the  two  liquids,  the  fresh  water,  by  its  specific 
lightness,  floats  on  the  surface  of  the  sea  to  a distance  of 
many  miles  from  the  land. 


WAVES. 

151.  Waves  are  the  risings  and  fallings  of  the  water, 
caused  by  some  power,  such  as  the  blowing  of  the  wind. 
The  power,  whatever  it  happen  to  be,  communicates  a force 
to  the  mass  of  liquid,  and  a series  of  undulations  is  the 
consequence. 

152.  These  undulations,  or  waves,  exhibit  the  transmis- 
sion of  the  communicated  force.  The  force  does  not 
advance  or  alter  the  lateral  position  of  the  water  at  any 
given  point;  it  only  alters  the  water  in  its  vertical  position, 
or  in  relation  to  its  depth.  When  therefore  waves  advance, 
the  water  does  not  advance  with  them ; the  water  but  rises 
and  falls,  and  assumes  the  figure  of  undulations  on  its 
surface.  When  the  undulations  approach  the  shore,  the 
water  then  acquires  a progressive  motion,  where  it  is  shal- 
,ow,  and  by  friction  on  the  bottom  or  impulsion  against 


110.  How  are  under  currents  explained  1 

111.  What  is  peculiar  in  the  undulations  of  waves  ? 


ALTERATION  OF  TEMPERATURE. 


51 


the  shore,  the  communicated  force  is  exhausted.  4 lie 
shaking  of  a carpet  affords  an  exact  representation  of  the 
action  of  waves  or  undulations. 

153.  Waves  are  comparatively  superficial ; they  seldom, 
even  in  the  greatest  storms,  rise  to  a height  of  more  than 
twelve  feet  above  the  level  of  calm  water,  and  make  an 
equal  descent  beneath,  making  altogether  an  appearance  of 
twenty-four  feet ; at  eight  or  ten  feet  below  the  hollow  or 
trough  of  the  waves  the  water  is  tranquil.  Waves  “ moun- 
tains high”  is  only  a figure  of  speech. 

ALTERATION  OF  TEMPERATURE. 

154.  By  altering  the  temperature  of  liquid  bodies,  they 
become  liable  to  peculiar  laws,  and  exhibit  peculiar  pheno- 
mena. 

155.  At  a temperature  of  40  degrees  of  Fahrenheit’s 
thermometer,  water  is  at  the  point  of  greatest  density. 
When  the  temperature  is  reduced  below  this  point,  the 
liquid  gradually  increases  in  volume  till  it  reaches  32, 
when  it  freezes.  When  the  temperature  is  raised  above 
40,  the  volume  increases  till  it  reaches  the  boiling  point, 
at  which  it  has  extended  to  the  extent  of  l-22d  additional 
to  its  bulk. 

156.  In  consequence  of  this  expansibility  in  heating,  hot 
or  warm  water  is  specifically  lighter  than  cold  water ; there- 
fore, in  heating  any  mass  of  water  in  a vessel  over  a fire, 
the  lighter  or  warmed  particles  rise  to  the  top,  while  the 
cold  and  heavy  particles  sink  to  the  bottom  to  be  heated, 
and  to  rise  in  their  turn.  In  this  manner  the  process  of 
heating  proceeds,  until  all  the  particles  are  of  an  uniform 
temperature,  which  is  at  the  boiling  point,  when  the  liquid 
gradually  flies  off  in  steam. 

157.  If  water  be  heated  by  the  action  of  fire,  or  the  sun’s 
rays  on  its  upper  surface,  the  mass  is  longer  in  attaining 
the  vaporific  point  than  when  heated  below,  because  water 
is  a bad  conductor  of  heat,  and  therefore  the  heat  penetrates 
with  difficulty  through  the  upper  stratum  of  warmed  liquid  to 

1 12.  What  of  the  height  of  waves  ? 

113.  How  is  the  density  of  water  in  different  temperatures? 

114.  What  of  gradually  heating  water  over  the  fire  1 


52 


HYDRAULICS. 


reach  that  which  is  beneath  ; and  if  the  mass  be  very  large, 
as  for  instance  the  ocean,  no  intensity  of  heat  applied  above 
can  warm  it  throughout,  or  to  any  considerable  depth. 

158.  In  the  present  treatise,  our  only  consideration  is 
the  motion  of  the  liquid  while  heating,  or  in  consequence 
of  the  application  of  heat. 

15i».  This  motion  consists  in  the  rising  of  the  heated 
portion  of  the  water  to  the  top,  where  it  remains  till  cooled, 
when  it  is  liable  to  be  displaced  from  its  position. 

160.  No  mass  of  water  can  possibly  be  at  rest,  if  of  a 
higher  temperature  below  than  above,  so  long  as  the  tem- 
perature exceeds  40  degrees.  An  upward  and  descending 
motion  continues  till  the  uniform  temperature  has  been 
established,  whatever  be  the  size  or  shape  of  the  containing 
vessel. 

161.  In  consequence  of  the  tendency  in  water  to  assume 
an  uniform  temperature  in  all  parts  of  its  volume,  a plan 
has  been  devised  for  heating  houses  by  means  of  a hot- 
water  apparatus.  A long  winding  iron  pipe  is  carried 
from  the  top  of  a house  to  the  bottom ; there  it  passes 
through  a fire,  and  thence  rises  to  the  top  of  the  house 
again,  where  the  two  extremities  may  be  made  to  meet  in 
a small  cistern  or  filler.  In  such  a tube,  water  may  be 
made  to  boil,  or  at  least  to  attain  a high  temperature 
throughout  its  whole  extent. 

162.  Figure  25  is  a rude  outline  of  a hot-water  apparatus 

of  this  kind.  P is  the 
iron  pipe,  with  the  fil- 
er T at  the  top.  F is 
the  fire  beneath,  acting 
on  the  pipe.  The  pro- 
jections R R give  an 


the  pipe  into  rooms  or 
passages.  In  the  appa- 
ratus as  usually  erect- 
ed, the  pipes  are  of 


1 15.  How  is  it  when  heated  at  its  upper  surface  ? 

116.  What  of  the  motion  of  water  by  heat  ? 

117.  Explain  the  diagram  and  its  principles. 


AIR. 


53 


about  an  inch  in  diameter,  and  are  made  to  wind  in  all 
directions  round  the  walls  of  rooms  and  passages,  in  their 
progress  from  the  top  to  the  bottom  of  the  edifice.  The 
degree  of  heat  which  is  maintained  in  the  water  warms  the 
atmosphere  in  the  apartments,  and  obviates  the  use  of  fires. 

163.  Certain  currents  or  sets  of  the  ocean  are  known  to 
be  produced  by  the  etfort  to  attain  an  equability  of  tempe- 
rature throughout.  The  power  of  the  sun’s  rays  at  and 
near  the  equator  heats  the  sea  in  that  part  of  its  volume,  to 
the  depth  of  two  or  three  hundred  feet.  This  upper  stra- 
tum of  heated  water  flows  in  currents  towards  the  north 
and  south  poles,  and  there  to  a certain  extent  tempers  the 
severity  of  the  cold.  The  waters  of  the  northern  and 
southern  tracts  of  ocean,  displaced  by  these  currents,  neces- 
sarily sink  below  them,  and  push  on  towards  the  equator, 
to  supply  the  deficiency  caused  by  the  departure  of  the 
waters  above.  Thus,  in  the  economy  of  nature  we  see  a 
process  in  constant  action  precisely  the  same  in  principle 
as  that  upon  which  the  artificial  hot-water  apparatus  has 
been  established. 

Having  now  discussed  Hydrostatics  and  Hydraulics,  we 
come  to  the  kindred  subject  of  Pneumatics,  for  which,  as 
will  be  observed,  we  have  reserved  a notice  of  - certain 
hydraulic  machines  involving  pneumatical  agency. 

PNEUMATICS. 

GENERAL  DEFINITIONS. 

164.  Pneumatics,  from  the  Greek  word  Pneuma,  breath 
or  air,  is  the  name  of  the  department  of  science  which 
relates  to  the  weight,  pressure,  or  motion  of  air,  or  of  any 
aeriform  or  gaseous  fluids. 

165.  It  was  anciently  supposed  that  the  air  of  the  atmo- 
sphere was  an  element  or  simple  substance  in  nature.  It 
is  now  satisfactorily  established  that  air  is  not  an  elemen- 

118.  How  do  the  same  principles  act  in  nature? 

119.  Define  Pneumatics. 

120.  Is  air  compounded,  and  of  what  elements  ? 


54 


PNEUMATICS. 


tary  body,  but  is  composed  of  certain  gases  in  intimate 
union,  and  these  gases  can  be  separated  from  each  other  by 
a process  in  art.  The  investigation  of  this  subject  belongs 
to  Chemistry.* 

166.  Air,  in  its  common  condition,  is  a thin  transparent 
fluid,  so  subtile  that  it  cannot  be  handled,  and  when  at  rest 
it  cannot  be  felt. 

167.  That  it  is  a body,  however,  is  quite  obvious,  because 
we  feel  its  impression  or  force  when  agitated  as  wind,  or 
when  we  wave  our  hand  quickly  through  it.  In  the  quick 
motion  of  the  hand,  we  feel  that  it  is  partially  opposed  by 
something;  and  in  inhaling  breath  into  the  lungs,  we  feel 
t hat  we  are  drawing  something  through  the  mouth — that 
something  is  air. 

168.  Air,  like  every  other  substance,  whether  solid  or 
fluid,  possesses  a certain  gravity  or  weight.  The  weight  of 
air  certainly,  bulk  for  bulk,  is  much  less  than  that  of  water; 
still  the  weight  may  be  accurately  computed.  A bottle  full 
of  air  weighs  heavier  in  a balance  than  a bottle  of  the  same 
capacity  from  which  the  air  has  been  extracted. 

169.  A cubic  foot  of  water,  as  has  been  mentioned  (78), 

* Pure  air  consists  almost  entirely  of  nitrogen  and  oxygen  gases, 
with  a very  small  portion  of  carbonic  acid  gas.  Of  100  parts  of  air, 
reckoning  by  weight,  75.55  parts  are  nitrogen,  23.32  oxygen,  and  1.13 
carbonic  acid  and  watery  vapour.  Both  as  respects  weight  and  bulk, 
nitrogen  forms  the  chief  ingredient  of  the  atmosphere.  Air  is  rendered 
impure  by  fetid  odours  and  other  exhalations,  which  it  has  the  power 
of  holding  to  a certain  extent.  Animal  respiration  chemically  changes 
the  constitution  of  air  ; oxygen  is  destroyed  or  deposited  in  the  blood, 
and  carbonic  acid  is  given  out  in  its  stead.  Thus,  we  inhale  pure  air, 
and  exhale  that  which  is  foul.  As  every  full-grown  person  inhales 
about  400  cubic  inches  of  air  per  minute,  the  tendency  of  respiration 
(not  to  speak  of  loss  by  combustion)  to  deteriorate  the  atmosphere  may 
be  easily  conceived.  Nature,  however,  abounds  in  provisions  for  pre- 
serving atmospheric  purity.  We  need  here  only  notice  the  beneficial 
effects  of  winds,  the  vast  extent  of  ocean  over  whose  surface  is  an 
inexhaustible  reservoir  of  pure  air,  the  purification  by  electric  agency, 
and  the  influence  of  light  or  the  solar  rays.  By  whatever  means  effected, 
it  is  certain,  from  experiment,  that  the  air  now  consists  of  the  same 
ingredients,  and  in  the  same  proportion,  as  it  did  fifty  years  ago. 


121.  How  is  the  material  character  of  air  proved  ? 

122.  How  is  the  purification  of  air  explained  1 (Note). 

123.  How  is  it  proved  that  air  has  weight  ? 

121.  What  relation  does  it  bear  to  water  in  gravity  1 


GENERAL  DEFINITIONS. 


■weighs  1000  ounces.  A cubic  foot  of  air  weighs  only  523 
grains,  being  a little  more  than  one  ounce  ; water,  therefore, 
is  about  840  times  heavier  than  the  air  of  our  atmosphere. 

170.  Inasmuch  as  water  is  a standard  for  comparing  the 
gravities  of  liquids,  air  is  a standard  in  the  same  respect  for 
all  aerial  substances. 

171.  The  specific  gravity  of  air  being  denominated 
1000,  oxygen  gas  is  1111 ; nitrogen  gas  972;  hydrogen  gas 
69;  and  carbonic  acid  gas  1529.  The  lightest  of  these 
kinds  of  gas,  therefore,  is  hydrogen,  and  the  heaviest  car- 
bonic acid.  Hence  if  indefinite  quantities  of  these  aeriform 
bodies  were  placed  in  a vessel,  or  in  an  apartment,  we 
should  find,  that,  after  certain  portions  had  gone  into  inti- 
mate union,  according  to  the  laws  by  which  they  combine, 
the  surplus  portions  of  each  would  assume  relative  positions 
according  to  their  respective  weights — the  heaviest  to  the 
bottom,  and  the  lightest  to  the  top.  Such  an  experiment 
would  resemble  that  previously  noticed,  of  the  mixture  of 
mercury,  oil,  water,  and  spirits  (74). 

172.  Air  and  all  kinds  of  gases  are  rendered  lighter  by 
the  application  of  heat,  for  then  the  particles  in  the  mass 
are  repelled  from  each  other,  and  occupy  a greater  space; 
this  process  of  lightening  or  thinning  is  called  rarefaction. 
Rarefied  air,  being  specifically  lightest,  mounts  above  that 
of  a common  density.  The  warmest  air  is  always  at  the 
top  of  a room,  and  the  coldest  at  the  bottom. 

173.  Air  is  distinguished  from  water  not  only  by  its 
extreme  comparative  lightness,  but  the  property  of  elasti- 
city ; it  is  a compressible  and  elastic  fluid. 

174.  When  any  quantity  of  air  is  compressed  into  a 
smaller  space  than  it  naturally  occupies,  it  will  return  to 
its  natural  bulk  on  the  pressure  being  withdrawn. 

175.  A small  bladder  of  air  may  be  squeezed  between 
the  hands  so  as  to  be  considerably  reduced  in  size;  and  on 
opening  the  hands  again,  and  wilhdrawing  the  pressure,  it 
will  instantly  resume  its  former  bulk.  If  a metallic  tube 
or  barrel  be  fitted  with  a moveable  plug  or  piston,  which  is 

125.  How  is  the  specific  gravity  of  gases  computed  ? 

126.  What  effect  does  heat  produce  on  air  ? 

127.  What  of  the  elasticity  of  air,  with  an  example  I 


5G 


PNEUMATICS. 


made  to  work  in  it  per  ectly  air-tight,  the  air  which  occu- 
pies the  space  between  the  top  and  the  bottom  of  this 
barrel  when  the  piston  enters,  can  be  compressed  to  a hun- 
dredth part,  or  even  less,  of  its  usual  bulk.  If  the  force, 
however,  by  which  the  piston  is  pushed  down,  be  with- 
drawn, the  air,  by  its  elasticity,  will  force  it  up  again  with 
a power  equal  to  that  by  which  its  descent  was  resisted. 

170.  In  proportion  as  any  given  volume  of  air  is  dimin- 
ished by  pressure,  its  elastic  force  is  increased;  in  other 
words,  the  elastic  force  or  elasticity  of  air  is  proportional 
to  its  density. 

THE  ATMOSPHERE. 

177.  The  air,  as  formerly  expressed,  is  a great  ocean 
wrapped  round  the  earth  to  a depth  of  from  forty-five  to 
fifty  miles  above  the  highest  mountains,  and  forms  a men- 
struum which  is  essential  to  the  existence  of  all  animals 
and  plants. 

178.  This  ocean  of  air  penetrates  into  all  unoccupied 
places,  in  the  same  manner  as  water  flows  into  all  crevices 
and  holes  beneath  the  level  of  its  surface  ; and  it  also  finds 
a place  in  the  bodies  of  animals,  plants,  and  liquid  sub- 
stances; hardly  any  thing,  indeed,  that  we  see  in  nature  or 
art,  is  free  from  air,  unless  force  has  been  employed  to 
extract  it. 

179.  The  height  of  the  atmosphere,  though  usually  esti- 
mated at  forty-five  or  fifty  miles,  is  in  reality  unknown.  The 
highest  point  above  the  level  of  the  sea,  which  has  ever  been 
reached  by  any  human  being,  is  21,000  feet,  which  has 
been  attained  in  a balloon. 

180.  It  is  only  conjectured,  from  the  refraction  of  the 
sun’s  rays  and  other  circumstances,  that  the  height  of  the 
atmosphere  is  about  fifty  miles.  At  and  near  the  level  of 
the  ocean  it  is  most  dense,  in  the  same  manner  as  water  at 
the  bottom  of  the  sea  is  more  dense  than  it  is  at  the  surface 
on  account  of  the  incumbent  pressure.  As  we  ascend 


128.  How  is  the  elasticity  of  gases  computed  ? 

129.  What  of  the  atmosphere  and  its  importance  and  universality  T 

130.  What,  of  its  height  and  density  at  different  altitudes  ? 


THE  ATMOSPHERE. 


57 


mountains,  or  in  any  other  way  penetrate  upwards  into  the 
atmosphere,  the  air  becomes  gradually  less  dense,  and  so 
thin  is  it  at  the  height  of  three  miles  on  the  summit  of 
Mont  Blanc,  that  breathing  is  there  performed  with  some 
difficulty.  Beyond  this  limited  height,  the  density  of  the 
air  continues  to  diminish,  and  at  the  elevation  of  about 
fifty  miles,  it  is  believed  to  terminate. 

181.  The  extreme  height  of  the  atmosphere  is  not  ob- 
servable from  the  situation  in  which  we  are  placed  on  the 
earth.  Our  eye,  on  being  cast  upwards,  perceives  only  a 
vast  expanded  vault,  tinted  with  a deep  but  delicate  blue 
colour;  and  this  in  common  language  is  called  the  sky. 
The  blueness  so  apparent  to  our  sense  of  sight  is  the  action 
of  the  rays  of  light  upon  the  thin  fluid  of  the  upper  atmo- 
sphere, and  the  brightness  is  in  proportion  to  the  absence 
of  clouds  and  other  watery  vapours 

182.  In  proportion  as  the  spectator  rises  above  the  surface 
of  the  earth,  and  has  less  air  above  him,  and  that  very  rare, 
the  blue  tint  gradually  disappears,  and  if  he  could  attain  a 
height  at  which  there  is  no  air,  say  at  above  fifty  miles  in 
height,  the  sky  would  appear  perfectly  dark  or  black.  Tra- 
vellers who  have  ascended  to  great  heights  on  lofty  moun- 
tains, describe  the  appearance  of  the  sky  from  these  elevated 
stations  as  dark  or  of  a blackish  hue.* 

183.  The  atmosphere  possesses  the  capacity  for  absorb- 
ing and  sustaining  moisture,  but  only  to  a limited  extent. 
When  saturated  to  a certain  degree,  it  is  relieved  by  the 
falling  of  the  moisture  in  the  form  of  rain.  It  is  calculated 
that  the  whole  atmosphere  round  the  globe  could  not  retain 
at  one  time  more  moisture  than  would  produce  about  six 
or  seven  inches  of  rain. 

184.  By  an  elevation  of  temperature,  the  capacity  of  the 
atmosphere  to  absorb  and  sustain  moisture  is  increased,  and 
by  a lowering  of  temperature,  decreased.  Cold  breezes, 
by  lowering  the  temperature  of  the  air,  cause  the  aeriform 
moisture  to  assume  the  appearance  of  clouds,  and  then  to 

* See  Treatise  on  Optics. 

131.  What  of  the  blueness  of  the  sky  ? 

132.  What  of  moisture  and  the  capacity  of  the  atmosphere  ? 

133.  How  does  temperature  affect,  it  ? 


58 


PNEUMATICS. 


fall  as  rain.  Clouds  disappear  in  fine  weather,  and  again 
appear  when  it  is  cold.  When  a cloud  descends  on  the 
side  of  a hill,  it  gradually  enters  a region  of  warmth  or 
higher  temperature,  and  disappears;  but  when  a cloud 
ascends  a hill,  it  enters  a region  of  cold,  and,  consequently, 
being  condensed,  it  is  precipitated  as  a shower  of  rain. 
Hence  the  old'familiar  rhyme — 

When  the  clouds  go  up  the  hill, 

They’ll  send  down  water  to  turn  a mill. 

185.  Thus,  the  atmosphere  is  the  great  field  in  which 
the  varied  phenomena  of  clouds,  rainbows,  meteors,  and 
other  appearances  in  the  sky,  are  exhibited.  As  respects 
the  phenomena  of  light  itself,  the  atmosphere  acts  a most 
important  part.  Received  in  it,  the  rays  of  the  sun  are 
harmoniously  diffused  in  all  directions  through  it,as  through 
a thick  crystalline  body,  and  afford  light  in  situations  which 
otherwise  would  be  in  darkness.  The  atmosphere,  there- 
fore, which  an  ignorant  person  might  suppose  to  be  nothing, 
is  as  invaluable  a constituent  of  creation  as  land  or  water; 
it  is  a fluid  essential  for  the  existence  of  animals  and 
plants ; it  affords  a field  for  all  kinds  of  meteorological  phe- 
nomena ; it  is  a supporter  of  combustion,  and  an  important 
agent  for  the  diffusion  of  heat  and  light,  and  also  for  the 
transmission  of  sound. 

We  shall  now  briefly  enumerate  the  laws  of  aerial  fluids, 
which  it  will  be  observed  resemble  those  of  liquid  bodies. 


PNEUMATICS— CONTINUED. 

LAWS  OF  AIR. 

186.  First — The  pressure  of  the  air  is  equal  in  all  direc- 
tions: Second — Its  degree  of  pressure  depends  on  the  ver- 
tical height  or  depth,  and  at  any  place  is  proportional  to  its 
density : 'fhird — Its  surface  is  level  in  all  parts  of  its 


134.  What  phenomena  are  dependent  on  the  atmosphere  1 

135.  Name  the  law's  of  aerial  fluids. 


PRESSURE  OF  AIR. 


50 


volume:  Fourth — It  affords  support,  according  to  its  den- 
sity and  to  the  weight  of  the  fluid  displaced. 

1ST.  That  air  presses  equally  in  all  directions,  may  be 
rendered  evident  by  filling  a bladder  with  that  fluid,  and 
then  pressing  upon  it  so  as  almost  to  make  it  burst.  The 
pressure  is  freely  communicated  through  the  mass,  as  in 
the  case  of  the  bag  of  water  (21),  and  it  will  be  observed 
that  the  confined  air  will  rush  out  with  equal  impetuosity 
at  whatever  part  you  make  a hole  in  the  surface. 

188.  The  level  of  surface  of  air  is  less  perfect  than  the 
uniform  level  of  water,  on  account  of  the  greater  elasticity 
of  the  substance.  In  a series  of  strata  of  air  of  different 
densities,  one  above  the  other,  a small  portion  of  each 
mingles  with  those  which  immediately  adjoin  it — the  pani- 
cles of  one  commingle  to  a certain  extent  with  those  of 
another.  There  is  thus,  as  respects  aerial  bodies,  a modi- 
ficaiion  of  the  law  of  uniform  levelness  of  surface  in  all 
parts  of  the  volume  of  fluid. 

PRESSURE  OF  AIR. 

189.  The  pressure  depending  on  the  vertical  height  or 
depth  of  air,  is  an  important  property  in  the  atmosphere, 
and  on  it  depends  the  explanation  of  numerous  phen  imena. 

190.  Air  being  a substance  possessing  gravity,  it  must 
of  necessity  press  downwards  in  the  direction  ol  the  centre 
of  the  earth;  and  therefore  the  degree  of  pressure  on  any 
given  point  will  be  equal  to  the  weight  of  the  column  of 
air  above  the  point,  and  proportional  to  the  density  of  the 
air  at  that  point. 

191.  The  idea  of  the  atmosphere  possessing  the  property 
of  gravity  or  pressure,  is  of  comparatively  modern  date.  No 
such  notion  was  entertained  by  the  ancients,  in  consequence 
of  living  animals  being  observed  to  move  with  perfect  ease 
in  all  directions,  and  because  there  was  no  other  appearance 
in  nature  calculated  to  suggest  it  to  their  minds. 

192.  It  was,  however,  remarked,  that,  when  the  air  w:as 


• 36.  What  of  the  equal  pressure  of  air,  and  its  exact  level? 
137.  How  is  atmospheric  pressure  computed  and  proved  ? ' 


60 


PNEUMATICS. 


sucked  out  of  a small  glass  tube,  the  lower  end  of  which 
was  immersed  in  water,  the  water  rushed  up  into  the  tube 
and  occupied  the  situation  of  the  displaced  air.  In  conse- 
quence of  this  and  similar  phenomena,  it  was  alleged  as  a 
doctrine  in  physics,  that  “ nature  abhors  a vacuum.” 

193.  A vacuum  is  a space  destitute  of  air  or  any  other 
kind  of  matter;  and  the  notion  was,  that  whenever  by  any 
chance  such  an  empty  space  was  found,  nature  interposed 
with  all  imaginable  haste  to  fill  it.  With  this  very  rude 
idea,  pumps  were  formed  to  raise  water,  the  rising  of  the 
water  in  these  instruments  being  ascribed  simply  to  nature’s 
abhorrence  of  a vacuum.  At  length  it  was  discovered  that 
water  could  not  be  drawn  up  by  a pump  above  a height 
of  about  thirty-two  feet,  and  that  a vacuum  above  that  ele- 
vation remained  unfilled;  whereupon  the  terms  of  the  doc- 
trine were  changed,  and  it  was  said  that  nature  abhorred  a 
vacuum  only  to  a height  of  thirty-two  feet,  but  no  farther. 

194.  This  explanation  was  seemingly  unphilosophical, 
and  men’s  minds  being  carefully  turned  to  the  subject, 
various  experiments  were  performed,  and  the  important 
truth  became  manifest,  that  the  atmosphere  possessed  gra- 
vity or  pressure  ; also,  that  that  pressure  w'as  the  sole  cause 
of  the  rushing  of  liquids  into  tubes  exhausted  of  air — the 
height  of  the  ascending  liquids  being  in  every  case  limited 
by  the  degree  of  pressure  of  the  incumbent  atmosphere. 
Thus,  the  discovery  of  a simple  truth  in  science  at  once 
abolished  the  fantastic  doctrine  of  nature’s  abhorrence  of  a 
vacuum,  and  all  the  laboured  sophistry  with  which  it  was 
supported.*  Nature  has  no  dislike  to  a vacuum  ; a vacuum 
will  occur  in  all  situations  from  which  solids  or  fluids  are 
accidentally  or  artificially  excluded. 

195.  The  degree  of  pressure  imposed  by  the  atmosphere 
on  any  given  spot  on  the  earth’s  surface,  as  already  noticed 
(190),  is  equal  to  the  weight  of  the  column  of  air  above 

* This  great  discovery  in  physical  science  was  made  by  Torricelli, 
an  eminent  Italian  mathematician,  about  the  year  1644.  It  was  sug- 
gested by  an  ineffectual  attempt  to  raise  water  from  a deep  well  near 
Florence,  by  means  of  a pump  of  a greater  height  than  thirty-two  feet. 


138.  What  of  the  maxim,  “ nature  abhors  a vacuum  ?” 

139.  How  did  Torricelli  discover  atmospheric  pressure  1 


PRESSURE  OF  AIR. 


Cl 


that  spot,  and  is  also  proportional  to  the  density  of  the  air 
at  the  place.  The  atmosphere  is  deepest  or  of  greatest 
vertical  height  at  the  level  of  the  ocean,  and  there  it  exerts 
the  greatest  pressure.  The  pressure  of  the  air  at  the  level 
of  the  sea  is  usually  reckoned  to  be  about  15  pounds  on 
every  square  inch.* 

19G.  The  pressure  of  15  lbs.  to  the  square  inch  refers  to 
every  shape  of  surface  at  or  near  the  sea’s  level.  The 
pressure  is  sidewise,  upward,  oblique,  and  in  every  other 
direction,  as  well  as  downward,  because  fluids  press  equally 
in  all  directions.  Thus,  in  every  crevice,  nook,  or  vessel, 
in  which  air  happens  to  be,  the  pressure  is  equally  intense. 
The  human  being,  for  example,  sustains  the  pressure  of  15 
lbs.  to  the  square  inch  all  over  his  person,  and  this  is  a 
load  under  which  he  could  not  possibly  move,t  unless  the 
pressure  was  also  exerted  in  the  interior  of  his  body,  or 
through  his  whole  system  of  muscles,  viscera,  and  bones, 
by  which  means  the  external  pressure  is  counteracted,  and 
he  feels  no  pressure  whatever. 

197.  if,  however,  the  air  by  any  means 
be  withdrawn  from  the  interior  of  any  object 
that  object  becomes  immediately  susceptible 
oi  the  external  atmospheric  pressure.  There 
are  many  familiar  examples  of  this  pressure 
around  us.  One  of  the  most  common  con- 
sists in  causing  a thimble  to  adhere  to  the 
hand  by  sucking  the  air  from  beneath  it : 
the  adhesion  is  the  result  of  the  pressure  of 
the  atmosphere  on  the  exhausted  space  on 
the  hand.  Another  consists  in  lifting  a stone 
by  means  of  a sucker,  formed  of  a string  and 
Figure  26.  a wetted  piece  of  leather,  as  in  the  accompa- 

* The  actual  pressure  varies  from  14  lbs.  to  15  lbs.,  according  to 
circumstances.  By  various  authorities  it  is  stated  at  14.7  lbs.  For 
convenience,  we  siate  it  throughout  in  the  text  at  15  lbs. 

t The  body  of  a man  has  a surface  of  2000  square  inches,  and  there- 
fore the  pressure  upon  him  is  equal  to  30,000  lbs. 

140.  What  of  the  degree  of  this  pressure  and  where  the  greatest? 

141.  How  much  to  the  square  inch  ? 

142.  In  what  directions  is  the  pressure  exerted  ? 

143.  Why  do  we  not  feel  this  enormous  pressure  ? 

144.  Explain  the  diagram. 


62 


PNEUMATICS. 


nying  figure.  The  wetted  leather  is  in  this  case  pressed 
down  upon  the  stone,  and  the  string  is  then  pulled:  if  air 
were  admitted  under  the  end  of  the  string,  the  sucker  would 
come  off,  but  none  being  admitted,  the  atmosphere  presses 
on  the  sucker,  a rigid  adhesion  of  the  sucker  to  the  stone 
is  produced,  and  the  stone,  if  not  too  heavy,  is  lifted. 

08.  The  surgical  process  of  cupping  is  upon  the  same 
principle.  A small  glass  cup  is  held  with  its  mouth  near 
the  part  to  be  operated  on,  and  the  air  being  consumed 
within  it  by  a lighted  taper,  it  is  instantly  applied,  and  ad- 
heres with  great  force.  The  part  having  been  previously 
lanced,  the  blood,  rushing  to  fill  the  vacuum,  enters  the  cup 
in  copious  small  streams.  The  feeling  endured  in  cupping 
is  that  of  considerable  weight. 

10‘J.  The  feet  of  fiies  and  some  other  insects  are  formed 
on  the  principle  of  the  sucker,  by  which  means  they  are 
enabled  to  walk  and  run  with  security  on  the  ceiling  of  an 
apartment,  back  downwards,  or  on  an  upright  and  smooth 
pane  of  glass.  At  each  step  in  advance,  they  procure  a 
hold  by  the  formation  of  a vacuum  or  air-tight  space  beneath 
their  leet.  The  rapidity  with  which  these  vacuums  or  air- 
tightnesses are  formed  and  destroyed  is  an  exceedingly 
interesting  phenomenon  in  the  economy  of  the  animal,  and 
cannot  be  rivalled  by  the  utmost  efforts  of  human  skill.  On 
a very  moderate  computation,  a fly,  in  travelling  six  feet  in 
the  space  of  a minute,  creates  and  destroys  as  many  as 
10,000  vacuums.  When  deprived  of  the  outer  extremities 
of  its  legs,  on  which  the  apparatus  for  adhesion  is  situated, 
a fly  can  walk  without  any  apparent  difficulty  on  a hori- 
zontal surface,  such  as  a table,  but  is  quite  incapable  of 
adhering  to  the  roof,  or  of  climbing  any  upright  surface. 

200.  Limpets,  snails,  and  some  other  crustaceous  animals, 
adhere  to  rocks  and  stones,  by  causing  a vacuum  within 
their  shells,  which  they  accomplish  by  shrinking  into  a 
smaller  bulk  ; by  this  simple  contrivance,  nature  has  effec- 
tually provided  for  their  safe  adhesion  to  their  appropriate 
places  of  residence. 

145.  What  other  examples  are  cited  ? 

146.  What  of  flies  walking  on  the  ceiling  ? 

147.  How  is  a vacuum  formed  by  certain  animals  1 


THE  AIR-PUMP. 


63 


THE  AIR-PUMP. 

201.  Air  may  be  artificially  withdrawn  from  a containing 
vessel  by  means  of  an  apparatus  called  the  air-pump.  This 
apparatus  is  usually  small,  lor  standing  on  a table,  and  con- 
sists chiefly  of  a glass  jar  called  a receiver,  placed  mouth 
downwards  over  a flat  surface,  and  with  a small  brass  pump 
to  draw  the  air  from  it.  The  annexed  cut,  Figure  27, 

represents  an  outline  section 
of  an  air-pump,  the  working 
of  which  may  be  described. 
R is  the  glass  receiver  stand- 
ing on  a flat  and  smooth 
plate  SS,and  fitting  so  exactly 
that  no  air  can  penetrate  be- 
tween the  edges  of  the  recei- 
ver and  the  plate.  In  the  plate 
SS,  th;  re  is  a channel  AB 
issuing  into  the  barrel  of  a 
pump.  P is  the  piston  of  the 
pump,  with  its  rod  C above, 
which  is  moved  upwards  and 
downwards  bv  a handle  and 
winch.  The  rod  C works  in 
a tight  collar  D.  At  the  bot- 
Figure  27.  tom  Qf  the  pump  there  is  a 

»alve  V,  by  which  the  air  is  to  escape,  and  prevented  from 
again  entering.  On  depressing  the  piston,  a portion  of  the 
contained  air  is  expelled  by  the  valve,  and  on  raising  the 
piston  again  to  its  position  at  the  top,  another  column  ■ f 
air  is  admitted  from  the  receiver  into  the  pump,  which  is 
expelled  in  its  turn.  Thus,  by  a process  of  expulsion,  the 
air  in  the  receiver  becomes  at  every  stroke  downwards  more 
rire,  till  at  length  a vacuum  sufficient  for  all  practical  pur- 
poses is  established.  The  valve  V,  which  opens  outwards, 
is  kept  forcibly  shut  at  every  rising  of  the  piston  by  external 
pressure  of  the  atmosphere. 


148.  Describe  an  air-pump,  and  its  use. 

149.  What  experiments  are  cited  1 


04 


PNEUMATICS. 


202.  By  means  of  the  air-pump,  a number  of  interesting 
experiments  in  pneumatics  may  be  performed.  For  exam- 
ple, if  a bladder,  half  full  of  air,  and  tightly  tied  at  the  neck, 
be  placed  under  the  receiver,  and  a vacuum  then  produced, 
the  air  in  the  bladder  will  expand  by  the  removal  of  the 
external  pressure,  and  seem  as  if  ready  to  burst.  Dried 
raisins,  during  a similar  operation,  will  expand,  and  have 
all  the  plumpness  of  new  fruit ; and  an  egg,  by  the  expan- 
sion of  its  confined  air,  will  explode.  Any  small  animals, 
such  as  mice,  placed  below  the  receiver,  and  deprived  of 
air,  will  immediately  die,  both  from  want  of  breath  and  the 
expansion  of  their  bodies. 

203.  The  atmosphere  serves  to  retard  the  falling  of  bodies 
of  a light  and  porous  nature,  and,  therefore,  in  the  exhausted 
receiver  of  an  air-pump,  all  such  bodies  descend  with  the 
same  velocity  as  bodies  of  a heavy  compact  nature.  A piece 
of  coin  and  a feather  let  fall  at  the  same  instant  of  time, 
from  a hook  within  the  top  of  an  exhausted  receiver,  will 
strike  the  bottom  at  the  same  moment.* 

204.  That  atmospheric  air  is  useful  for  the  transmission 
of  sound,  in  the  absence  of  other  media,  is  also  exemplified 
by  the  air-pump.  If  we  place  a small  bell  in  a receiver  in 
such  a manner  as  to  admit  of  being  rung  easily  from  the 
outside,  without  admitting  air  into  the  inside,  whilst  the 
receiver  is  full  of  air  the  sound  of  the  bell  will  be  distinctly 
heard ; but  after  the  receiver  has  been  exhausted,  and 
although  the  bell  be  struck  with  the  same  force,  the  sound 
will  be  inaudible,  or  nearly  so.  If  a small  portion  of  air 
be  admitted,  it  will  be  faintly  heard,  and  it  will  gradually 
increase,  according  to  the  quantity  of  air  which  is  allowed 
to  enter  the  receiver.  Thus,  we  are  indebted  to  the  air  as 
a medium  for  conveying  to  us  the  sound  of  each  other’s 
voices,  and  all  the  melodious  notes  which  constitute  music. 

205.  The  act  of  inspiring  and  expiring  air  resembles  the 
alternating  action  of  an  air-pump.  The  air,  on  being  drawn 
in  through  the  appropriate  tubes,  fills  the  lungs,  and  the 

* Laws  of  Matter  and  Motion,  paragraphs  173,  174,  175. 


150.  How  is  air  shown  to  be  necessary  for  transmitting  sound  l 

151.  What  animal  function  resembles  the  air-pump? 


AIR-GUN'.  65 

chest  is  expanded ; having  performed  its  office,  the  air  is 
expelled  in  an  impure  condition,  leaving  a partial  vacuum 
within,  until  another  inspiration  causes  another  expansion. 

206.  A machine,  called  a condensing  pump  or  syringe, 
is  formed  tor  the  purpose  of 
showing  experiments  with  air 
more  dense  than  that  of  the 
common  atmosphere.  The  ap- 
paratus, which  is  represented 
in  Figure  28,  consists  of  a 
close  glass  jar  or  receiver  fixed 
in  a framp.  A wire  and  hook 
serve  to  communicate  with  the 
interior  during  the  perform- 
ance of  experiments.  The 
syringe  i is  wrought  by  a piston 

Figure  28.  with  ^g  handie  From  the 

bottom  of  the  syringe  there  is  a tube  communicating  with 
the  interior  of  the  receiver.  When  the  piston  is  raised,  a 
valve  beneath  opening  inwards  admits  air  into  the  cylinder 
of  the  syringe,  and  when  it  is  depressed,  this  quantity  of 
air  is  forced  into  the  receiver;  by  the  alternate  raising  and 
depressing  of  the  piston,  an  immense  quantity  of  air  is 
forced  into  the  receiver. 

207.  The  elastic  force  of  air  so  condensed  is  very  great, 
and  is  employed  for  the  projection  of  balls  from  an  instru- 
ment called  an  air-gun.  A certain  quantity  of  compressed 
air  is  confined  in  a chamber  at  the  inner  end  of  the  barrel, 
and  when  allowed  to  escape  by  touching  a valve,  a bullet 
is  projected  with  a force  resembling  that  by  gunpowder. 

208.  The  explosive  force  of  gunpowder  itself  is  nothing 
else  than  the  sudden  disengagement  of  air  from  the  particles 
of  the  powder. 


152.  Explain  the  diagram. 

153.  What  of  an  air-gun,  and  of  gunpowder  itself? 


66 


PNEUMATICS. 


PNEUMATICS  CONTINUED. 

PRESSURE  OF  AIR  ON  SOLIDS  AND  LIQUIDS. 

209.  The  pressure  of  the  atmosphere  affects  all  liquid 
as  well  as  solid  bodies.  The  load  of  the  incumbent  air  is 
as  sensibly  exerted  within  any  given  mass  of  water  as  on 
the  surface.  Thus,  atmospheric  pressure  keeps  water  and 
other  liquids  at  the  density  they  are  usually  seen  to  possess. 

210.  If  a glass  be  filled  with  water,  and  placed  under  the 
receiver  of  an  air-pump,  the  abstraction  of  the  air,  by  the 
removal  of  the  atmospheric  pressure,  will  cause  the  water 
to  expand  or  become  less  dense,  and  it  will  overflow  the 
vessel  in  which  it  is  contained. 

211.  Water  in  its  ordinary  condition  contains  a certain 
quantity  of  particles  of  air  mixed  up  with  it.  When  the 
atmospheric  pressure  is  lightened,  these  particles  o air 
expand,  and  being  of  a less  specific  gravity  than  water,  they 
mount  to  the  top  of  the  liquid  in  the  form  of  small  globules, 
and  so  fly  off.  The  same  effect  is  produced  by  expanding 
water  by  means  of  heat ; the  globules  of  air  rise  to  the  sur- 
face, and  escape  or  remain  attached  to  the  inside  of  the 
vessel.  Crystal  bottles  of, water  may  be  observed  to  be 
covered  inside  with  small  air-bells  when  the  weather  be- 
comes suddenly  light  or  warm.  Water  which  has  been 
boiled  is  comparatively  free  of  air,  and  has  an  insipid 
flavour. 

212.  Certain  gases  are  generated  in  some  liquors,  such 
as  in  porter,  beer,  and  champagne  wine,  and  unless  the 
bottles  in  which  they  are  contained  be  of  sufficient  strength 
to  endure  the  expansive  tendency,  they  will  burst.  On 
drawing  the  cork  from  a bottle  of  one  of  these  liquors,  the 
confined  gas  or  air  is  suffered  to  expand,  and  the  contents 
gush  forth,  a mixture  of  froth  and  liquid.  If  the  liquid 
remain  in  an  open  glass  for  a short  time,  a large  portion  of 


154.  How  is  air  shown  to  exert  pressure  within  liquids  ? 

155.  What  proofs  have  we  that  water  contains  air  ? 

156.  What  of  gases  generated  in  certain  liquors  ? 


PRESSURE  ON  SOLIDS  AND  LIQUIDS. 


07 


the  long-confined  gases  escapes  into  the  atmosphere,  and 
the  liquor  seems  flat  or  dead.  A portion  of  confined  air, 
however,  still  remains  in  consequence  of  the  atmospheric 
pressure.  If  we  take  a glass  of  ginger-beer  which  seems 
quite  dead,  and  place  it  under  the  exhausted  receiver  of  an 
air-pump,  it  will  again  froth  and  appear  brisk. 

213.  Some  mineral  waters  on  springing  from  the  ground 
sparkle  like  beer.  These  most  likely  rise  from  great 
depths,  where  the  incumbent  pressure  is  considerable,  and 
on  attaining  the  surface  of  the  earth  they  expand,  and  give 
forth  the  air  pent  up  in  their  mass. 

214.  If  a bladder  full  of  air  be  carried  from  a low  situa- 
tion to  a great  height,  the  contained  air  will  expand,  and 
the  bladder  will  burst,  the  same  as  if  placed  under  the 
exhausted  receiver  of  an  air-pump. 

215.  If  a bladder  be  filled  with  air  at  a great  height, 
where  the  fluid  is  rare,  and  brought  to  a low  situation,  the 
contained  air  will  be  compressed  by  the  more  dense  fluid 
without,  and  the  bladder  will  appear  as  if  only  half  or  par- 
tially filled. 

216.  The  fluids  in  the  animal  and  vegetable  system  are 
similarly  affected  by  atmospheric  pressure.  Our  bodies, 
for  instance,  would  expand,  and  our  blood-vessels  probably 
be  ruptured,  if  placed  for  a short  time  in  a vacuum.  On 
the  same  principle,  any  change  in  the  density  of  the  atmo- 
sphere has  an  effect  on  the  animal  frame. 

217.  The  atmospheric  pressure,  in  ordinary  conditions 
of  the  air,  and  at  the  level  of  the  sea,  as  already  stated,  is 
equal  to  15  lbs.  to  the  square  inch.  If  by  any  means, 
such  as  digging  into  the  earth,  we  should  go  below  the 
sea’s  level,  the  weight  will  be  found  to  increase.  In  deep 
coal  mines,  for  instance,  the  pressure  of  the  atmosphere  is 
something  more  than  15  lbs.  to  the  square  inch. 

218.  The  pressure  diminishes  in  a similar  degree  as  we 
ascend  into  the  atmosphere.  At  every  step  upwards  from 
the  shore,  the  burden  of  the  superincumbent  mass  lightens. 

157.  What  of  mineral  waters  1 

158.  How  of  the  experiments  with  a bladder  ? 

159.  How  are  the  fluids  of  the  body  affected  ? 

160.  How  mav  the  pressure  be  increased,  or  diminished  f 


68 


PNEUMATICS. 


At  the  height  of  three  miles,  one-half  of  the  weight  is  lost ; 
or  in  other  words,  at  that  height  the  air  is  only  half  the 
density  of  air  at  the  sea’s  level. 

219.  The  breathing  apparatus  of  animals  is  suited  to  an 
atmospheric  density  and  pressure  such  as  is  found  at  the 
sea’s  level,  or  at  a moderate  elevation  above  it.  By  ascend- 
ing in  the  atmosphere,  as  in  climbing  hills,  we  are  deprived 
of  the  quantity  of  air  to  which  we  have  been  accustomed; 
and  when  we  reach  a height  of  three  miles,  we  in  reality 
inhale  only  one-half  of  the  weight  of  air  into  the  lungs  that 
we  use  at  the  sea’s  level.  Consequently,  those  who  ascend 
to  great  elevations  experience  difficulty  in  breathing,  and 
feel  an  expansion  in  their  blood-vessels  and  muscles  by  the 
removal  of  a portion  of  the  ordinary  pressure.*  All  the 
joints  in  our  bodies,  particularly  those  of  the  knee  and 
shoulder,  are  in  a great  measure  held  together  by  the  exter- 
nal pressure  of  the  atmosphere;  and  thus  a principle  in 
Pneumatics  compensates  for  a loading  of  muscular  ligaments. 

220.  A consideration  of  the  effects  of  atmospheric  pres- 
sure, and  its  variability  at  different  elevations,  also  the 
alterations  in  pressure  caused  by  the  expansion  or  lightening 
of  the  air  by  heat,  and  its  increased  density  by  cold  and 
moisture,  tends  to  explain  the  remarkable  influence  which 
change  of  climate  has  upon  the  human  constitution.  Thus, 
the  inhabitants  of  countries  possessing  a light  dry  atmo- 
sphere are  usually  more  lively  than  those  of  countries  with 
a heavy  moist  climate. 

PRESSURE  ON  MERCURY THE  BAROMETER. 

221.  The  pressure  of  the  atmospheric  column,  at  any 
given  point,  may  be  weighed  with  considerable  exactness, 

* It  is  known  that  travellers,  and  even  their  practised  guides,  often 
fall  down  suddenly  as  if  struck  by  lightning,  when  approaching  lofty 
summits,  on  account  chiefly  of  the  thinness  of  the  air  which  they  are 
breathing,  and  some  minutes  elapse  before  they  recover.  In  the  ele- 
vated plains  of  South  America,  thednhabitants  have  larger  chests  than 
the  inhabitants  of  the  lower  regions — another  admirable  instance  of  the 
animal  frame  adapting  itself  to  the  circumstances  in  which  it  is  placed. 
— ArnotVs  Physics. 


161.  How  are  animals  affected  by  atmospheric  pressure  ? 

162.  What  of  the  effects  of  a change  of  climate  ? 


PRESSURE  ON  MERCURY THE  BAROMETER. 


GO 


by  balancing  it  against  an  opposite  column  of  mercury, 
water,  or  other  liquid. 

222.  The  pressure  of  15  lbs.  to  the  square  inch  at  the 
ocean’s  level  is  found  by  experiment  to  be  equal  to  the 
weight  of  a column  of  mercury  of  30  inches  in  height,  a 
column  of  water  33  feet  in  height,  or  a column  of  oil  37 
feet  in  height.  In  other  words,  the  burden  of  the  whole  of 
our  atmosphere  is  equivalent  to  an  ocean  of  mercury  cover- 
ing the  earth  to  a height  of  30  inches,  an  ocean  of  waier  to 
a height  of  33  feet,  or  an  ocean  of  oil  to  a height  of  37 
feet. 

223.  The  fact  of  such  being  the  degree  of 
atmospheric  pressure  admits  of  easy  proof,  by 
means  of  a glass  tube  upwards  of  thirty-two 
inches  in  length,  and  a cup  half  filled  with  mer- 
cury, as  represented  in  Figure  29.  The  tube  is 
close  at  its  upper  end  at  B,  but  open  at  its  lower 
extremity,  which  is  immersed  in  the  mercury 
below  the  surface  level  C P D.  The  tube  having 
in  the  first  place  been  filled  with  pure  mercury, 
a finger  is  placed  on  its  open  end  to  prevent  the 
egress  of  the  liquid,  and  thus  held,  the  lower 
end  of  the  tube  is  turned  downwards,  and 
plunged  into  the  vessel  of  mercury,  when  the 

^finger  is  removed  from  the  orifice.  The  mercury 
in  the  tube  will  now  be  observed  to  fall  to  E, 
or  the  height  of  about  thirty  inches  above  the 
"h  surface  CPD,  and  there  it  will  remain. 

224.  The  questi  >n  now  arises,  Why  the  mer- 
cury in  the  tube  does  not  run  out  altogether  into  the  cup, 
instead  of  standing  to  a height  of  thirty  inches  in  the 
tube?  The  explanation  of  the  phenomenon  is,  that  from 
E to  B in  the  tube  is  a vacuum,  and  therefore  the  mercury 
at  its  upper  extremity  is  entirely  free  of  atmospheric  pres- 
sure— there  is  no  superincumbent  weight  to  push  it  out. 
The  column  of  mercury  EP  presses  with  nothing  but  its 


Fig.  29. 


163.  How  may  the  atmospheric  pressure  be  weighed  1 

164.  What  calculations  are  stated  ? 

165.  Explain  the  diagram  and  its  design. 


TO 


PNEUMATICS. 


own  weight  on  the  mercury  of  the  cup.  This  weight  of 
thirty  inches  of  mercury  is  counterbalanced  by  the  pressure 
of  air  on  the  surface  of  the  mercury  in  the  cup ; and  thus 
it  is  evident  that  the  weight  of  the  atmosphere  is  equivalent 
to  the  weight  of  thirty  inches  of  mercury.  If  by  any  means 
we  remove  the  atmospheric  pressure  from  the  mercury  in 
the  cup,  the  mercury  in  the  tube  will  immediately  sink 
into  the  cup. 

225.  The  circumstance  of  the  column  of  mercury  in  the 
tube  being  narrow,  and  the  surface  of  the  mercury  in  the 
cup  being  broad,  makes  no  difference  in  the  experiment, 
because  the  pressure  of  elastic  fluids  is  as  their  density,  not 
as  width  of  volume.  The  same  result  would  occur  if  the 
surface  of  the  mercury  presented  to  the  atmospheric  pres- 
sure were  only  the  width  of  the  tube. 

226.  The  height  at  which  mercury  stands  in  a tube  of 
this  kind,  always  bears  reference  to  the  incumbent  weight 
of  the  atmosphere  on  the  open  and  lower  extremity  of  the 
column.  If  we  increase  the  external  pressure  by  artificial 
means,  or  by  descending  below  the  sea’s  level,  the  mercury 
rises;  if  we  decrease  it  by  artificial  means,  or  by  ascending 
into  the  atmosphere,  or  if  the  atmosphere  is  rarefied  by  heat,  » 
the  mercury  falls. 

227.  This  very  obvious  connection  between  the  rising 
and  falling  of  mercury  in  a tube,  and  the  atmosphere,  has 
suggested  the  construction  of  an  instrument  called  the 
Barometer  (a  word  from  the  Greek,  signifying  iceight  and 
measure ),  by  which  the  effects  of  atmospheric  pressure  may 
be  accurately  known. 

22S.  The  barometer  in  common  use  consists  of  a narrow 
glass  tube  upwards  of  thirty  inches  in  length,  and  bent 
upwards  at  its  lower  extremity,  as  represented  in  Figure 
30.  The  mercury  is  introduced  into  the  tube  with  great 
care,  so  that  a perfect  vacuum  exists  at  the  upper  extre- 
mity. The  surface  of  the  mercury  in  the  bent  part  is  open 
to  the  action  of  the  atmosphere,  and  buoys  up  a small 
plummet  or  float  F,  to  which  a thread  is  attached;  the 
thread  proceeds  upwards  to  a small  pulley  G,  over  which 


166.  What  instrument  has  been  constructed  on  this  principle  ? 


PRESSURE  ON  MERCURY THE  BAROMETER. 


71 


it  goes,  and  terminates  in  a small  ball  W.  The  friction  of 
the  thread  on  the  pulley  turns  a small  index 
H,  which  points  to  figures  on  the  surrounding 
dial.  Commonly,  the  whole  apparatus,  except 
the  dial  plate,  is  concealed  in  an  ornamental 
frame. 

229.  Barometers  of  this  description  are  ad- 
justed in  such  a manner  that  the  smallest 
rising  or  falling  of  the  mercury  from  atmo- 
spheric action,  affects  the  index  on  the  dial, 
and  shows  the  degree  of  pressure. 

239.  In  common  circumstances,  the  mer- 
cury ranges  from  29  to  30  inches.  It  seldom 
sinks  so  low  as  28  or  rises  to  31.  When  it 
falls,  an  indication  is  given  of  diminished 
pressure,  and  as  diminished  pressure  causes 
the  air  to  expand,  and  consequently  to  be 
sensibly  cooled,  moisture  is  liable  to  be  pre- 

Figure  30.  Cipitated  in  the  form  of  rain  (184).  Hence 
a fall  in  the  mercury  of  the  barometer  is  considered  a 
prognostic  of  rain  or  wet  weather,  and  a rise  the  reverse. 
The  dial  of  the  barometer  is  marked  accordingly. 

231.  The  barometer,  besides  being  a weather-glass,  is 
used  as  an  instrument  for  measuring  the  heights  of  moun- 
tains, or  heights  attained  in  balloons,  above  the  level  of  the 
sea. 

232.  As  the  entire  atmosphere  sustains  thirty  inches  of 
mercury  in  the  tube,  it  follows  that  at  every  step  as  we 
ascend,  the  pressure  will  become  less,  and  a less  body  of 
mercury  be  sustained.  It  is  found  that  at  the  height  of 
five  hundred  feet  the  mercury  has  sunk  half  an  inch.  But 
the  fall  does  not  proceed  in  this  ratio  as  we  go  upwards, 
because  a half  of  the  whole  atmosphere  is  within  about 
three  miles,  and  the  other  half  expanded  to  an  altitude  of 
about  fifty  miles.  Hence,  on  gaining  a height  of  three 
miles,  the  mercury  is  found  to  have  sunk  to  fifteen  inches, 


167.  Explain  the  diagram. 

168.  What  are  the  indications  of  this  instrument  ? 

169.  To  what  other  uses  is  it  adapted  ? 

170.  What  of  ascending  to  a great  altitude  ? 


72 


PNEUMATICS. 


or  one  half,  and  on  gaining  a height  of  four  miles,  to 
‘vvelve  inches. 

233.  Barometers  for  measuring  heights  are  constructed 
with  a determined  scale,  marked  along  the  tube  of  mercury, 
and  by  consulting  it  as  we  ascend,  we  learn  the  height  of 
any  spot  that  we  may  reach.  Perfect  exactness,  however,  is 
not  to  be  expected  in  this  mode  of  measurement,  because 
the  atmospheric  pressure  is  liable  to  variation  from  tempera- 
ture, and  the  mercury  is  liable  to  contraction  or  expansion 
from  the  same  cause.  To  guard  against  error,  a thermo- 
meter, as  well  as  a barometer,  is  consulted  in  ascending 
heights,  and  the  indications  of  both  instruments  according 
to  a scale  established  by  experiment,  determine  the  degree 
of  elevation.  Thus,  for  a diminution  of  one  degree  of 
temperature  between  0 and  32  degrees,  the  mercury  in  the 
barometer  falls  0.0034  of  an  inch,  and  between  32  degrees 
and  52  degrees  it  rises  0.0033  of  an  inch. 

PRESSURE  ON  WATER PUMPS. 

234.  The  effect  of  atmospheric  pressure  on  water  is 
observable  in  various  contrivances  in  the  arts. 

235.  Fill  a glass  to  the  brim  with  water,  and  lay  a piece 
of  paper  over  the  whole  surface  of  the  liquid ; then  turn  the 
glass  carefully  upside  down,  holding  on  the  paper  by  the 
hand  ; the  water  will  now  remain  in  the  glass,  being  upheld 
by  the  pressure  of  the  atmosphere  against  the  paper. 

236.  Glass  fountains  of  water  for  bird-cages,  ink-holders, 
and  reservoirs  of  oil  for  lamps,  are  constructed  on  the  prin- 
ciple of  the  liquid  being  upheld  by  atmospheric  pressure. 

237.  The  apparatus  for  lifting  water  from  wells,  forming 
the  common  sucking-pump,  acts  on  the  principle  of  remov- 
ing the  atmospheric  pressure  from  a column  of  the  liquid, 
thus  causing  a vacuum  in  the  pump,  and  allowing  the 
atmospheric  pressure  on  the  surface  of  the  liquid  in  the 
well  to  force  up  and  balance  the  column  of  liquid. 

238.  Figure  31  represents  the  outline  of  a common 


171.  How  may  perfect  exactness  be  attained  ? 

172.  What  examples  of  atmospheric  pressure  J 


PRESSURE  ON  WATER PUMPS. 


li 


Figure  31. 


sucking-pump.  It  consists  of  a cylinder,  furnished  witli  a 
piston  A made  to  fit  air-tight.  In 
this  piston  there  is  a valve  opening 
upwards,  notseen  in  the  cut.  When 
the  piston  is  raised,  the  air  is  rare- 
fied more  and  more  at  each  stroke  m 
that  portion  of  thecylinder  through 
which  it  has  moved  upwards,  and 
the  pressure  of  the  air  upon  the 
surface  of  the  water  on  the  outside 
of  the  tube  forces  the  fluid  into  it. 
The  valve  B is  at  the  same  time 
opened  upwards,  and  the  water 
after  several  strokes  rushes  in  above 
it.  When  the  upward  stroke  of  the 
piston  is  complete,  it  is  again  de- 
pressed, the  water  passes  through 
the  valve  in  the  piston  ; and  on  the  next  stroke,  it  is  dis- 
charged at  the  spout.  It  is  evident,  that,  when  the  piston 
is  sunk  downwards,  the  water  cannot 
be  again  forced  out  of  the  pump, 
because  the  valve  at  the  bottom  is 
pressed  down,  and  prevents  its  es- 
cape. 

239.  Water  may  in  this  manner 
be  lifted  by  a pump  to  any  height, 
but  in  each  case  the  lower  or  fixed 
valve  in  the  pump  must' be  less  than 
34  feet  from  the  surface  of  the  water. 
It  is,  however,  disadvantageous  to 
lift  water  from  great  depths  by  this 
means.  In  such  cases,  therefore,  it 
is  usual  to  employ  a succession  of 
pumps  one  above  another. 

Figure  32.  240.  It  is  customary  to  call  pumps 

hydraulic  machines ; properly  speaking,  they  are  both 


173.  Explain  the  first  diagram. 

174.  Are  pumps  merely  hydraulic  machines  1 

175.  What  of  the  forcing  pump,  and  its  uses  ! 


74 


PNEUMATICS. 


hydraulic  and  pneumatic  machines,  for  water  is  raised  by 
them  in  a great  measure  through  the  agency  of  atmospheric 
pressure. 

241.  The  form  of  pump  used  for  forcing  water  to  a 
height  above  the  ground,  as  in  the  case  of  fire-engines  or 
portable  forcing-pumps  for  gardens,  is  different  from  the 
common  suction-pump.  The  object  in  the  forcing-pump 
is  to  lift  water  to  a certain  height  by  the  formation  of  a 
vacuum,  and  then  to  inject  it  with  violence  into  the  air. 

242.  The  action  of  the  forcing-pump  apparatus  is  repre- 
sented in  Figure  32.  The  piston  A sucks  the  water  by  its 
upward  motion;  but  on  depressing  it,  the  valve  B is  closed, 
and  the  water  is  consequently  forced  through  the  pipe  C. 

243.  In  the  case  of  supplying  water  to  the  boiler  of  a 
steam-engine,  it  is  necessary  to  employ  a forcing-pump,  in 
order  to  overcome  the  pressure  of  steam  within  the  boiler. 
The  force  with  which  the  water  is  injected  overcomes  the 
tendency  which  the  steam  has  to  rush  out. 

244.  Cold  or  moderately  warm  water  can  only  be  lifted 
by  a pump.  If  the  water  be  above  a certain  temperature, 
about  150  degrees  at  the  utmost,  the  sucker  cannot  form  a 
perfect  vacuum,  because,  in  the  attempt  to  do  so,  the  water 
yields  a steam  or  vapour  which  fills  the  space;  in  other 
words,  by  removing  the  atmospheric  pressure  by  the  piston, 
the  water  begins  to  vaporize  as  if  about  to  boil.  When  a 
pump  is  made  to  operate  upon  hot  water,  it  labours  in  vain 
to  raise  the  liquid.  This  circumstance  limits  the  heat  of 
water  injected  into  the  boilers  of  steam-engines;  or  if  the 
water  is  injected  at  a high  temperature,  it  must  receive  its 
heat  between  the  pump  and  the  boiler.  This  is  sometimes 
done,  by  causing  the  tube  from  the  pump  to  pass  through 
a vessel  of  waste  steam. 


SYPHONS. 

245.  Atmospheric  pressure  is  very  conspicuous  in  the 
case  of  the  syphon. 


176.  What  is  used  to  supply  water  to  the  boiler  of  a steam-engine, 
and  why  ? 

-7.  What  effect  has  hot  water  upon  a pump  7 


SYPHONS. 


246.  A syphon  is  a tube  bent  in  a particular  manner,  a id 
is  used  for  drawing  off  liquors  from  casks,  or  water  from 

A reservoirs.  One  kind  of  syphon  is  repre- 
sented in  Figure  34,  and  consists  of  a tube 
bent  into  two  equal  limbs,  each  open  at 
the  extremity.  If  such  a syphon  be  filled 
with  water  and  inverted,  so  as  to  turn  the 
two  orifices  downwards,  the  liquid  will 
not  run  out,  but  remain  suspended  in  the 
Figure  34.  tube,  because  the  pressure  of  the  column 
of  water  within  is  not  so  great  as  the  pressure  of  the  air 
without,  and  thus  its  escape  outwards  is  prevented.  If  one 
end  be  put  into  a vessel  of  water,  the  vessel  will  be  emptied 
down  to  a level  with  the  orifice.  It  is  evident  that,  when 
one  end  of  the  syphon  is  inserted  in  water,  the  pressure  of 
the  atmosphere  upon  the  surface  of  the  water  impels  the 
liquid  through  the  tube,  and  it  could  be  forced  upwards  to 
an  elevation  of  above  thirty  feet,  or  the  height  to  which 
water  rises  in  a vacuum.  The  diagram  represents  an  in- 
strument of  this  kind  furnished  with  two  cups,  firmly  attach- 
ed to  the  ends,  which,  by  retaining  a portion  of  the  liquid, 
keeps  the  syphon  always  full  and  ready  for  use. 

247.  Syphons  are  more  commonly  made  with  a long  and 
B short  limb,  as  in  Figure  35.  On  in- 

serting  the  short  limb  into  a vessel 

//  Vv, _ of  liquid,  and  drawing  the  air  out  of 

//  tU*3e  at  l^e  mout*1  the  liquid 

//  ifSilli  VV‘N  rush  out  a stream,  and  con- 
//  1 llill  I l'nue  fl°wing  the  vessel  is  emp- 

//  ' I |;M  t]  tied.  The  pressure  upwards  into  the 

//  tube  at  A is  the  excess  of  the  atmo- 

//  spheric  pressure  above  the  vertical 

pressure  of  the  column  of  fluid  AB  : 
/||  and  the  similar  pressure  at  C is  the 

Figure  35.  excess  of  the  atmospheric  pressure 

above  the  vertical  pressure  of  the  column  of  fluid  BC ; but 


178.  Explain  the  syphon  and  its  use. 

179.  Explain  the  diagram. 

ISO.  Explain  the  second  diagram. 


76 


PNEUMATICS. 


the  latter  excess  is  evidently  the  greater,  and  hence  the 
liquid  in  the  vessel  is  necessarily  forced  upwards  through 
the  tube  from  C to  B ; and  thus  the  vessel  is  drained  of  its 
contents.  By  placing  a stopcock  on  the  tube  above  A,  the 
stream  can  be  checked,  and  permitted  to  flow  at  pleasure. 
There  are  instances  of  towns- being  supplied  with  water  by 
means  of  large  syphons  of  this  kind.  In  these  cases  the 
syphon  is  brought  over  a rising  ground  from  a lake  or 
fountain  at  some  distance. 

SYPHON  - SPRINGS. 

248.  Certain  kinds  of  springs  are  accounted  for  on  the 
princq  ieof  the  syphon;  they  act  from  the  combined  effects 


Figure  36. 

of  a vacuum  and  atmospheric  pressure.  The  following  are 
examples: — Let  ABC,  Figure  36,  represent  a mountain, 
and  DEF  a hollow  in  its  centre  containing  water  G,  which 
flows  to  it  through  several  small  ducts,  HHHH.  Let  IF 
be  a natural  syphon,  one  end  of  which  is  connected  with 
the  water  at  a,  and  the  other  ramifies  into  diverse  branches, 
issuing  from  the  mountain  at  bbhb.  Let  K be  also  another 


181.  What  of  syphon  springs  ? 
1S2.  Explain  the  drawing. 


SYPHON  SPRINGS. 


77 


stream  issuing  from  the  hill  at  L,  but  which,  for  the  present, 
we  shall  suppose  is  closed  at  E.  Now,  if  the  hollow  cavern 
be  tilled  to  the  height  M by  the  rivulets  HHHH,  it  is  evi- 
dent that,  on  the  principle  of  the  syphon  above  described, 
the  hollow  will  be  emptied  to  the  level  N ; and  the  water 
thus  withdrawn  will  emerge  from  the  mountain  in  the  form 
of  springs  bbbb,  because  they  are  all  at  a lower  level  than 
that  to  which  the  water  rises  in  the  syphon  at  I'.  When 
the  whole  has  run  off,  they  will  then  cease  to  flow  until  the 
hollow  is  refilled  to  the  level  M,  when  it  will  flow  again, 
and  thus  the  process  goes  on.  This  is  what  is  termed  an 
intermitting  spring.  Some  springs,  called  variable  or  reci- 
procating, do  not  cease  to  flow,  but  only  discharge  a much 
smaller  quantity  for  a certain  time,  and  then  give  out  a 
greater  quantity.  This  arises  from  there  being  two  hollows, 
one  above  the  other,  in  the  bosom  of  the  mountain,  the 
highest  one  having  a runner,  not  of  a syphon  form,  which 
joins  the  stream  of  the  lower  one  beyond  the  bend,  or 
inflection  I'.  This  runner  keeps  the  stream  always  supplied 
to  a certain  degree,  although  the  lower  cavity  be  dry.  But 
when  the  latter  is  filled  to  M,  the  current  is  of  course  greatly 
augmented,  which  augmentation  continues  until  the  under 
hollow  is  again  drained. 

249.  In  some  places  there  are  springs  which  run  freely 
in  summer,  or  in  dry  weather,  and  almost  stop  in  winter, 
or  in  wet  weather.  This  is  explained  in  the  following 
manner  : — Suppose  the  passage  KL  to  be  now  open  at  E, 
and  the  water  in  the  hollow  to  be  very  low,  as  it  is  in  sum- 
mer, or  in  dry  weather — so  low  indeed  that  none  can  escape 
through  the  syphon  II' — then  the  spring  at  L will  flow 
constantly.  If  during  wet  weather,  however,  the  cavern  be 
filled  to  the  level  M,  the  syphon  will  act,  and  drain  off  the 
water;  and  if  we  suppose  the  mouth  of  the  syphon  to  be 
lower  than  the  outlet  at  E,  and  to  drain  off  as  much  as  the 
runners  HHHH  supply,  it  will  allow  none  to  issue  from 
the  orifice  at  L at  all,  for  then  E would  be  above  the  surface 
of  the  water. 


183.  What  variety  of  springs  are  named  ? 

184.  Recite  the  explanations  given. 


78 


PNEUMATICS. 


250.  The  orifice  at  L,  supposing  there  was  no  other 
outlet  from  the  mountain,  may  be  taken  as  an  instance  of 
those  springs,  most  common,  which  flow  continually.  The 
reservoir  from  which  these  are  supplied  is  generally  to  be 
traced  to  some  hill  or  range  of  hills  in  the  neighbourhood, 
which  from  the  quantity  of  rain,  &c.  collected  by  them, 
keep  the  internal  cavity  continually  full,  or  nearly  so. 
Springs  cannot  rise  higher  than  the  reservoir  from  which 
they  are  supplied,  and  fountains,  which  are  springs  that 
burst  out  at  a level  considerably  lower  than  the  water  in 
the  reservoir,  do  not  rise  so  high,  because  when  they  issue 
from  the  orifice,  they  have  the  resistance  of  the  air  to  over- 
come, which  retards  their  ascent.  The  current  also  branches 
out  laterally,  and  thus  the  force  which  impels  it  upwards  is 
partly  expended  in  giving  it  an  oblique  direction. 

251.  In  some  parts,  intermitting  springs  have  afforded 
an  opportunity  for  designing  individuals  imposing  upon  the 
credulous.  Taking  advantage  of  the  flowing  and  stopping 
of  water-runs,  these  persons  have  gained  credit  to  them- 
selves by  predicting  the  period  when  the  events  would  happen 
which,  from  a few  years’  observation,  would  easily  be  learned. 

PNEUMATICS  CONTINUED. 

BOILING  POINT  DETERMINED  BY  ATMOSPHERIC  INFLUENCE. 

252.  The  pressure  of  the  atmosphere  exerts  a powerful 
influence  over  the  forms  in  which  matter  presents  itself  to 
our  senses.  The  force  of  gravity  draws  bodies  towards 
the  earth,  and  the  atmospheric  pressure,  along  with  the 
property  of  cohesion  of  particles,  serves  to  give  them  com- 
pactness or  firmness.  By  removing  the  atmospheric  pres- 
sure, by  means  of  the  air-pump  or  otherwise,  some  solid 
bodies  will  become  soft  or  partially  liquid,  and  liquid 
bodies  will  evaporate  and  assume  an  aeriform  condition. 

253.  The  degree  of  pressure  exerted  by  the  atmosphere, 
and  also  the  degree  of  general  temperature,  are  adjusted  by 


1S5.  What  of  springs  and  fountains  as  to  their  height  ? 

186.  What  changes  result  from  removing  the  atmospheric  pressure  1 


BOILING  POINT ATMOjP H ERIC  INFLUENCE. 


73 


nature  to  produce  and  sustain  the  present  external  properties 
of  matter.  The  atmospheric  pressure  is  not  so  great  as  to 
prevent  spontaneous  evaporation  from  liquids,  but  is  suffi- 
cient to  moderate  its  action,  and  harmonize  it  with  other 
phenomena  in  nature. 

254.  Liquids  spontaneously  evaporate  at  all  temperatures 
from  the  freezing  point  upwards,  though  at  a much  slower 
rate  at  a low  than  a high  temperature.  When  the  liquids 
attain  that  temperature  at  which  the  phenomenon  of  boiling 
or  ebullition  occurs,  vaporization  is  in  greatest  activity,  and 
speedily  but  gradually  carries  off  the  particles  of  fluid  into 
the  atmosphere. 

255.  The  degree  of  heat  at  which  a liquid  body  boils, 
depends  on  the  amount  of  atmospheric  pressure,  and  also 
on  the  nature  of  the  body  itself.  The  constituent  particles  of 
certain  liquids  cohere  more  closely  together  than  others, 
and  a greater  heat  is  required  to  separate  them. 

256.  Subject  to  the  common  pressure  of  the  atmosphere, 
ether,  which  is  a volatile  liquid  used  in  medicine,  boils  at 
a temperature  of  104  degrees,  alcohol  or  strong  spirits  at 
170  degrees,  water  at  212  degrees,  tallow  at  about  600 
degrees,  and  mercury  at  692  degrees.  If  we  either  increase 
or  diminish  the  incumbent  pressure  as  given  by  the  atmo- 
sphere, the  boiling  points  of  these,  as  well  as  all  other 
liquids,  are  immediately  changed. 

257.  By  increasing  the  pressure  on  liquids  beyond  that 
given  by  the  atmosphere,  a greater  degree  of  heat  is  requi- 
red to  make  them  boil.  This  circumstance  is  taken  advan- 
tage of  in  the  case  of  certain  preparations,  in  which  a higher 
temperature  than  212  degrees  is  required.  For  example, 
to  extract  properly  the  gelatinous  and  oily  matter  from 
bones,  they  must  be  boiled  with  a quantity  of  water  in  a 
strong  closed  vessel;  the  steam  consequently  does  not 
escape,  but  presses  on  the  water,  and  so  keeps  it  from 
boiling  till  a very  high  temperature  has  been  attained.  The 
same  end  would  be  gained  by  forcing  in  air  upon  the  water 

187.  What  of  evaporation  and  vaporization  ? 

1S8.  Upon  what  does  the  boiling  point  of  liquids  depend  7 

189.  Name  the  boiling  point  of  different  liquids. 

190.  How  may  greater  heat  be  attained  without  boiling  7 


80 


PNEUMATICS. 


to  the  required  pressure,  as  for  instance,  to  a pitch  of  pres- 
sure of  B'J  lbs.  to  the  square  inch,  or  two  atmospheres. 

258.  By  endeavouring  to  boil  water  at  a point  below  the 
level  of  the  sea,  the  same  result  is  observable.  It  is  found 
that  in  a diving-bell  sunk  to  a depth  of  sixty-eight  feet  in 
the  sea,  water  does  not  boil  till  it  attain  a temperature  of 
272  degrees. 

25  J.  When  the  atmospheric  pressure  is  removed,  a con- 
trary effect  is  observable.  At  the  summit  of  Mont  Blanc 
water  boils  at  a temperature  of  187  degrees.  In  certain 
preparations  in  the  arts,  such  as  distilling  spirits,  and  extracts 
of  herbs  (for  scents  and  medicines),  it  is  important  to  have 
the  vaporific  point  at  a comparatively  low  temperature.  In 
all  such  cases  the  preparation  is  effected  in  a vacuum 
formed  by  an  air-pump  connected  with  the  boiling  liquid. 
Some  liquids  may  thus  be  boiled  at  a temperature  of  from 
90  degrees  to  100  degrees.  Unless  for  this  ingenious 
arrangement,  the  delicate  properties  of  some  medicines 
could  not  be  procured  by  distillation,  for  a heat  of  212 
degrees  would  injure  oi  destroy  them. 


STEAM. 

260.  Steam  produced  from  boiling  water  is  a transpa- 
rent, colourless,  and  invisible  substance,  like  air.  If  we 
could  look  into  the  boiler  of  a steam-engine,  we  should  see 
nothing  but  the  water  in  a state  of  ebullition.  The  white 
cloudy-looking  matter  which  is  emitted  in  the  form  of 
vapour,  is  moisture  produced  bv  the  partial  condensation 
of  the  steam  in  the  atmosphere — taking  the  form  of  vapour 
is  a step  towards  becoming  liquid  again. 

261.  A cubic  inch  of  water  produces  exactly  a cubic 
foot,  or  1728  cubic  inches,  of  steam,  at  212  degrees  of 
temperature ; in  other  words,  when  water  is  transformed 
into  steam,  it  occupies  1728  times  its  former  bulk.  In  this 
expanded  condition  steam  is  of  a less  specific  gravity  than 
air.  Its  density  is  expressed  by  0 625,  that  of  air  being  l 


191.  How  may  they  be  made  to  boil  at  lower  temperatures  ? 

192.  Define  steam,  and  vapour. 

193.  What  of  the  bulk  and  specific  gravity  of  steam  7 


LATENT  HEAT. 


81 


■262.  The  elastic  force  of  steam  in  the  process  of  heating 
— that  is,  the  force  with  which  it  seeks  to  expand — differs 
at  different  temperatures.  At  first  the  force  is  inconsider- 
able, but  it  rapidly  increases  as  the  temperature  is  raised. 
At  a temperature  of  212  degrees,  the  elastic  force  is  15 
lbs.  on  the  square  inch  of  the  containing  vessel,  or  equal 
to  the  external  pressure  of  the  atmosphere ; at  250  degrees 
it  is  30  lbs.,  at  272  degrees  it  is  45  lbs.,  and  at  290  degrees 
it  is  66  lbs. 

263.  As  the  elastic  force  increases,  so  does  the  density 
of  the  steam;  the  elastic  force,  indeed,  always  corresponds 
to  the  density;  because  the  more  steam  which  is  packed 
into  a given  bulk,  the  greater  must  be  its  expansive  force. 

264.  In  reference  to  steam-engines,  steam  of  different 
degrees  of  elastic  force  is  employed.  When  the  steam  is 
not  suffered  to  have  any  communication  with  the  atm  - 
sphere,  but  is  condensed  in  a vacuum  connected  with  the 
engine,  the  steam  employed  is  called  low  pressure.  In  most 
instances  its  elastic  force  is  not  more  than  15  lbs.  on  the 
square  inch;  and  as  this  is  counteracted  by  an  equal  pres- 
sure from  the  atmosphere,  there  is  no  danger  of  the  boiler 
exploding.  When  the  steam  is  not  condensed  in  this  man- 
ner, but  is  suffered  to  rush  out  in  puffs  into  the  atmosphere, 
it  must  possess  a force  not  only  to  move  the  engine,  but  to 
overcome  the  atmosphere  which  presses  upon  it  in  its 
emission.  To  possess  the  degree  of  force  called  high  pres- 
sure, the  steam  is  raised  to  a temperature  of  from  250 
degrees  to  272  degrees,  producing  an  elastic  force  of  from 
30  to  45  lbs.  on  the  square  inch  of  the  boiler.  Hence  the 
danger  of  explosion  in  working  high-pressure  engines. 

LATENT  HEAT. 

265.  The  change  of  form  in  bodies,  from  solid  to  liquid, 
and  liquid  to  gaseous,  or  from  liquid  to  solid,  and  gaseous 


194.  What  of  the  elastic  force  and  density  of  steam  ? 

195.  Explain  the  safety  of  low  pressure  engines,  and  why. 

196.  Whence  the  danger  of  high  pressure  ? 

197.  What  of  a change  of  form  in  all  bodies  ? 


82 


PNEUMATICS. 


to  liquid,  is  in  all  cases  attended  by  a remarkable  circum- 
stance in  relation  to  heat. 

266.  Heat  or  caloric,  as  already  mentioned,*  is  an  affec- 
tion or  quality  pervading  all  things,  but  frequently  concealed 
or  Intent,  in  which  state  it  is  in  no  respect  obvious  to  our 
senses,  and  cannot  be  detected  by  the  thermometer. 

267.  When  solids  become  liquids,  and  when  liquids 
become  airs,  latent  heat  is  evolved,  and  combines  with  the 
newly  formed  substances.  But  this  heat,  though  elabo- 
rated, is  still  latent,  not  perceivable  by  our  senses  or  by  the 
thermometer.  When,  on  the  other  hand,  liquids  become 
s lids  and  airs  become  liquids,  as  by  condensation,  the 
latent  heat  is  instantaneously  relieved  from  its  disguise,  and 
makes  itself  known. 

These  propositions  maybe  exemplified  as  follows  : — 

268.  YVhen  a vessel  of  water  open  to  the  atmosphere  is 
placed  on  the  fire,  the  water  gradually  becomes  hotter  till 
it  readies  212  degrees,  when  it  boils ; afterwards  its  tem- 
perature is  not  increased.  Now,  heat  must  be  constantly 
entering  from  the  fire,  and  combining  with  the  water  ; as 
the  water,  however,  does  not  become  hotter,  the  heat  must 
combine  with  that  part  of  it  which  flies  off  in  the  form  of 
steam  ; but  the  temperature  of  the  steam  is  only  2 12  degrees, 
the  same  as  the  water  from  which  it  rises,  and  therefore 
this  constantly  adding  heat  does  not  obviously  increase  its 
temperature. 

269.  Thus,  the  steam  which  rises  from  boiling  water 
becomes  a receptacle  for  the  heat  which  is  constantly  enter- 
ing the  liquid  from  the  fire,  and  in  this  receptacle  it  remains 
in  a dormant  or  latent  state,  till  the  steam  is  reduced  to 
vapour  or  its  elementary  liquid,  when  the  accumulated 
heat  is  instantaneously  developed.  The  scald  given  by 
steam  on  its  emission  into  the  atmosphere,  in  the  form  of 
vapour,  is  well  known  to  be  far  more  severe  than  that  given 
by  boiling  water.  The  deposition  of  the  latent  heat  from 

* Laws  of  Matter  and  Motion,  paragraph  78  to  SI. 


19S.  Explain  latent  heat,  and  when  it  is  evolved. 

199.  How  is  the  fact  exemplified,  and  what  of  scalds  ? 


LATENT  HEAT. 


83 


the  vapour  is  the  cause  of  this  excess  in  the  severity  of  the 
scald. 

270.  Dr.  Black,  professor  of  chemistry  in  the  University 
of  Edinburgh,  made  the  discovery  of  the  principle  of  latent 
h at,  about  the  year  1757.  The  following  was  one  of  his 
expcmnents: — He  put  some  water  at  a temperature  of  50 
degrees  m a tin-plate  vessel  upon  a red-hot  iron.  In  four 
minutes  it  began  to  boil,  and  in  twenty  minutes  it  was  all 
bmled  off.  During  the  first  four  minutes  the  water  received 
an  addition  of  4Jj  degrees  per  minute,  or  altogether  162 
degrees.  If  we  suppose  that  it  received  as  much  per  minute 
during  the  whole  time  of  boiling,  the  caloric  which  entered 
into  the  water,  and  converted  it  into  steam,  would  amount 
to  4H  multiplied  by  20,  which  is  810  degrees. 

271.  Water  may  be  heated,  as  already  stated  (257),  to  a 
temperature  of  more  than  212  degrees,  by  laying  a force 
upon  it  greater  than  that  imposed  by  the  atmosphere,  or  by 
simply  confining  the  steam  (allowing  no  emission  of  steam 
whatsoever),  which  has  the  same  elfect.  By  heating  water 
in  a strong  cylindrical  copper  vessel,  perfectly  closed,  called 
a Papin’s  Digester,  the  temperature  of  the  water  may  be 
raised  to  400  degrees  without  boiling.  If  the  mouth  of  the 
vessel  be  suddenly  opened  while  the  water  is  in  this  state, 
part  of  the  water  will  rush  out  in  tiie  form  of  steam,  but  the 
greater  part  remains  in  the  form  of  water,  and  its  tempera- 
ture instantly  sinks  to  212  degrees;  consequently,  188 
degrees  of  heat  have  suddenly  disappeared.  This  heat 
must  have  been  carried  otf  by  the  steam.  Now,  as  only 
about  one-fifth  of  the  water  is  converted  into  steam,  that 
one-fifth  must  contain  not  only  its  own  188  degrees,  but 
also  the  188  degrees  lost  by  each  of  the  other  four  parts  ; 
that  is  to  say,  it  must  have  contained  five  times  188  degrees, 
or  940  degrees.  Here,  then,  is  a proof  that  steam  contains 
at  least  943  degrees  of  heat. 

272.  If  one  part  of  steam,  at  212  degrees,  be  mixed  with 
nine  parts,  by  weight,  of  water  at  62  degrees,  the  steam 

200.  What  was  Dr.  Black’s  experiment  and  its  result  ? 

201.  How  may  water  be  heated  beyond  the  boiling  point  ! 

202.  By  what  instrument  may  this  be  done  ? 

203.  What  calculations  are  made  here  ? 


84 


PNEUMATICS. 


instantly  assumes  the  form  of  water,  and  its  temperature, 
after  mixture,  is  1786  degrees;  consequently,  each  of  the 
nine  parts  of  water  has  received  116  6 degrees  of  caloric, 
and  the  steam  has  lost  nine  times  1166  degrees,  or  1044 
degrees  of  caloric.  But  as  the  temperature  of  the  steam  is 
diminished  by  33-4  degrees,  we  must  deduct  this  sum, 
when  there  will  remain  rather  more  than  1000  degrees, 
which  is  the  quantity  of  heat  in  the  steam. 

273.  If  a gallon  of  water  be  transformed  into  steam,  and 
that  steam  allowed  to  mix  with  six  gallons  of  cold  water, 
the  whole  will  be  raised  to  the  boiling  point. 

274  From  these  and  other  philosophical  experiments,  it 
has  been  ascertained  that  the  latent  heat  in  steam  varies 
from  940  degrees  to  1044  degrees;  usually,  it  is  reckoned 
to  be  about  a medium  between  these  extremes,  or  nearly 
1000  degrees. 

275.  In  proportion  as  steam  is  raised  beyond  a tempera- 
ture of  212  degrees,  the  ratio  of  accumulation  of  latent 
heat  becomes  the  greater,  just  as  the  steam  becomes  more 
dense  and  of  greater  elastic  force.  At  a temperature  of 
290  degrees,  steam  will  rush  out,  and  deposit  four  times 
as  much  heat  as  it  would  do  at  212  degrees.  This  has 
been  ascertained  by  experiment. 

276.  To  prove  that  all  the  heat  above  212  degrees  is 
latent  in  steam,  it  is  only  necessary  to  place  a thermo- 
meter in  a boiler,  but  in  such  a way  that  it  can  be  seen 
through  a strong  piece  of  glass,  or  that  it  will  act  upon  an 
external  index.  Thermometers  with  externally  acting  in- 
dices are  common  in  steam  boilers. 

277.  We  can  now  comprehend  why  scalds  from  steam 
are  so  very  violent.  The  steam,  at  212  degrees,  so  long  as 
kept  within  the  boiler,  rises  to  a temperature  of  nearly  1000 
degrees  the  instant  it  comes  in  contact  with  the  air  or  any 
substance  on  which  it  condenses  itself.  Our  hand,  there- 
fore, on  suffering  a scald  from  steam,  receives  in  less  than 
a moment  of  time  1000  degrees  of  heat,  which  is  sufficient 
to  destroy  the  skin,  and  to  inflict  the  severest  pain. 


204.  What  is  the  latent  heat  in  steam  ? 

205.  Explain  the  illustration  here  gixen. 


LATENT  HEAT. 


85 


278.  In  the  process  of  evaporation  which  is  less  or  more 
in  constant  activity  over  the  globe,  the  aeriform  moisture 
carries  off  latent  heat  from  the  liquid  substances  from  which 
it  rises.  This  is  as  perceptible  by  our  sense  of  touch  or 
feeling,  as  the  deposition  of  heat  in  a scald.  If  we  wet 
the  back  of  our  hand  with  water,  we  feel  a sensation  of 
cold  from  the  evaporation  which  immediately  ensues.  If 
we  use  spirits  instead  of  water,  the  evaporation  will  be 
more  active,  and  the  sensation  of  cold  the  more  intense. 
The  feeling  of  cold  is  caused  by  the  withdrawal  of  heat 
from  the  part,  which  heat  becomes  latent  in  the  rising 
vapour.  Rooms  are  cooled  by  sprinkling  water  on  the 
floor;  the  coolness  being  caused  by  the  withdrawal  of  heat 
in  the  evaporation  which  ensues. 

279.  The  principle  of  latent  heat  is  essential  in  the  econ- 
omy of  nature.  The  mode  of  its  evolution  and  absorption 
has  the  effect  of  preventing  sudden  alterations  in  the  con- 
dition of  solids  and  liquids.  Instead  of  water  suddenly 
exploding  in  steam  on  attaining  the  boiling  point,  the 
process  of  transformation  into  air  is  gradual,  on  account 
of  the  steam  becoming  the  depository  of  the  accumulating 
heat.  So,  when  water  freezes,  it  does  not  do  so  instanta- 
neously on  attaining  the  freezing  point,  because  it  has  to 
absorb  the  heat  in  the  water,  and  seal  it  up  in  a latent 
state,  ready  to  be  developed  again  in  a manner  equally 
gradual  on  the  melting  of  the  ice.*  Thus  the  evolution 
and  absorption  of  latent  heat  form  an  important  principle 
in  regulating  change  of  condition  in  substances,  both  in 
the  economy  of  nature  and  of  art. 

PNEUMATICS  CONTINUED. 

ALTERATION  OF  TEMPERATURE  IN  AIR. 

We  have  now  to  consider  the  influence  of  change  of 
temperature  in  air. 

* Laws  or  Matter  and  Motion,  paragraph  117. 


206.  What  examples  of  latent  heat  are  cited  7 

207.  How  shown  in  nature  and  art  7 


86 


PNEUMATICS. 


280.  Air,  like  water,  is  heated  by  the  sun’s  rays,  and 
also  by  artificial  means. 

281.  The  heat  existing  in  any  given  bulk  of  air  depends 
on  the  quantity  or  weight  of  air  in  the  bulk. 

282.  In  some  situations  the  air  is  dense,  and  in  others 
it  is  thin — it  is  most  dense  where  the  atmospheric  pressure 
is  greatest,  or  at  the  level  of  the  sea. 

283.  If  we  take  a pound  weight  of  air  near  the  sea’s 
level,  and  another  pound  weight  at  a spot  a mile  above  the 
sea,  we  shall  tind  that  each  pound  contains  precisely  the 
same  quantity  o!  heat ; but  in  the  case  of  that  taken  near 
the  sea,  the  air  will  feel  warm,  and  in  the  case  of  the  other, 
the  air  will  feel  cool.  This  seems  paradoxical,  yet  it  is  a 
truth.  A pound  of  air,  taken  near  the  sea,  is  compact  in 
substance,  and  goes  into  a comparatively  small  bulk;  but 
that  taken  from  a high  part  of  the  atmosphere  is  thin,  and 
occupies  a much  larger  space. 

284.  This  explains  why  the  thin  air  on  high  grounds  is 
seemingly  colder  than  in  low  situations.  Aloft,  the  air  is 
as  warm  as  it  is  below,  but  there  is  less  of  it;  the  particles 
are  more  widely  asunder,  and  this  produces  the  effect  of  a 
greater  coldness.  Properly  speaking,  the  cold  in  high 
situations  arises  from  the  want  of  air,  rather  than  from  the 
air  itself. 

285.  In  the  warmest  regions  of  the  globe,  the  air  is  cold 
at  the  tops  of  high  mountains,  merely  because  the  air  is 
there  thin,  and  incapable  of  forming  a medium  for  the 
retention  of  heat  from  the  sun’s  rays.*  In  every  country 
there  is  a point  of  altitude  at  which  water  freezes  on  all 
occasions,  whether  summer  or  winter.  In  Europe,  this 
point — called  by  some  the  snow-line,  or  point  of  eternal 
snow — is  from  five  to  six  thousand  feet  above  the  level  of 
the  sea;  in  the  hot  regions  of  Africa  and  America,  it  is  at 

* The  thin  air  in  the  higher  regions  of  the  atmosphere  is  understood 
to  contain  heat  in  a latent  condition,  but  this  no  way  affects  the  above 
argument. 


208.  Bv  what  means  is  air  heated  1 

209.  What  relation  between  temperature  and  density  J 

210.  How  is  the  cold  in  high  situations  explained  ? 

21 1.  What  of  the  snow-line  in  different  countries  ? 


I 


LATENT  HEAT. 


87 


f >urteen  thousand  feet.  At  these  points  of  altitude  respec- 
tively, snow  lies  constantly  unmelted  on  the  mountain 
ridges  and  summits.  The  same  effect  is  observable  on 
ascending  in  a balloon.  In  the  warm  region  of  Hindostan, 
the  atmosphere  is  as  cool  and  pleasant  at  a certain  height 
on  the  Himalaya  mountains  as  it  is  in  the  northern  part  of 
Europe. 

286.  In  this  manner  we  see  that  atmospheric  pressure 
affects  the  temperature  in  the  air  around  us. 

2S7.  Inasmuch  as  heated  water,  from  its  specific  light- 
ness rises  to  the  top  in  any  containing  vessel,  while  the 
colder  particles  of  the  liquid  sink  to  the  bottom  (156),  so 
does  heated  air  from  precisely  the  same  cause  rush  upwards, 
while  the  colder  atmosphere  sinks  to  replace  it. 

288.  It  might  be  inferred  from  this  that  the  heated  air 
near  the  sea  and  other  low  situations  would  mount  into  the 
higher  regions  of  the  atmosphere,  and  there  sustain  a con- 
siderable warmth.  Heated  air  certainly  rises  into  the  upper 
strata  of  the  atmospuere,  but  on  rising  it  expands,  and  by 
that  very  circumstance  its  heat  has  no  sensible  effect  in 
meliorating  the  cold.  According  to  the  constitution  of 
things,  it  is  impossible  to  warm  the  higher  regions  of  the 
air.  The  quantity  of  heat  which  daily  ascends  all  over  the 
globe  is  immense,  but  it  never  in  the  smallest  degree  raises 
the  temperature  of  the  upper  air,  being  thrown  off  bv  radia- 
tion into  surrounding  space,  or  going  into  a latent  condi- 
tion. 

289.  The  air  differs  in  temperature  at  different  parts  on 
the  same  level,  in  consequenceof  the  constant  daily  shining 
and  withdrawal  of  the  sun’s  rays.  During  the  day  the  air 
is  warmed,  during  the  night  it  becomes  cool. 

290.  The  difference  of  temperature  produced  in  this  or 
any  other  manner,  leads  to  constant  disturbance  in  the  at- 
mosphere. Here  the  air  is  rising,  there  it  is  sinking  or 
rushing  sidewise  to  supply  the  deficiency ; in  short,  its 
motions  are  indescribably  various,  all  in  consequence  of 
the  ever-shifting  temperature  of  the  atmosphere. 


212.  What  analogy  between  liquids  and  gases  ? 

213.  Why  cannot  the  higher  regions  be  heated  ? 

214.  Explain  the  difference  between  day  and  night,  and  why  1 


88 


PNEUMATICS. 


AIR  IN  MOTION WINDS. 

291.  The  currents  of  the  air  are  called  winds.  Winds 
originate  from  any  cause  which  occasions  a portion  of  the 
atmosphere  to  expand  or  contract.  Change  of  temperature, 
as  being  the  principal  cause  of  these  expansions  and  con- 
tractions, is  the  principal  cause  of  winds.  The  manner  of 
the  origin  of  these  winds  is  very  simple,  and  is  completely 
exemplified  within  our  daily  experience.  When  the  door 
of  a heated  apartment  is  thrown  open,  a current  of  air  is 
thereby  immediately  produced : the  warm  air  from  the 
apartment  passing  out  and  the  cold  air  rushing  in. 

292.  Some  winds  occur  from  the  following  cause  : — 
When  a condensation  of  vapour  in  the  atmosphere  sudden- 
ly takes  place,  giving  rise  to  clouds  which  speedily  fall  in 
rain,  the  temperature  of  the  surrounding  air  is  sensibly 
altered,  and  the  colder  rushing  in  upon  the  warmer,  gives 
rise  to  a sudden  gust  of  wind.  For  this  reason,  a cold 
heavy  shower  passing  overhead,  with  a hasty  fall  of  snow 
or  hail,  is  often  attended  with  a violent  and  sudden  gust  of 
wind,  which  ceases  when  the  cloud  disappears,  but  is  re- 
newed when  another  cloud,  sweeping  along  in  the  same 
direction,  brings  with  it  a fresh  blast.  Accordingly,  a gust 
of  the  wind  is  universally  considered  to  be  a prognostic  of 
rain,  because  it  indicates  that  a change  is  taking  place  in 
the  temperature  of  the  atmosphere,  owing  to  the  vapour  in 
its  higher  regions  being  condensed  into  rain-clouds. 

293.  The  winds  which  blow  in  Great  Britain,  the  United 
States,  and  other  temperate  parts  of  the  earth,  generally 
originate  in  some  atmospheric  disturbance  on  the  ocean  or 
in  tropical  climates,  and  therefore  cannot  possibly  be  prog- 
nosticated with  any  degree  of  certainty. 

294.  The  most  remarkable  winds  are  those  which  tra- 
verse the  ocean  steadily  in  one  direction,  and  are  called 
“ trade-winds,”  from  their  use  to  mercantile  navigation.  In 
order  that  we  may  distinctly  understand  the  cause  and  na 

215.  Define  wind  and  its  causes. 

216.  Explain  the  connection  between  winds  and  rain. 

217.  Explain  the  trade-winds  and  their  source. 


AIR  IN  MOTION WINDS.  81) 

• 

ture  of  the  trade-winds,  it  is  necessary  to  bear  in  mind  that 
the  portion  of  the  globe  extending  23$  degrees  north  and 
23£  degrees  south  from  the  equator,  forming  the  torrid 
zone,  is  constantly  beat  upon  by  the  sun’s  rays  in  a direc- 
tion so  little  oblique,  that  the  most  intolerable  heat  might 
there  be  anticipated.  This  being  premised,  and  it  being 
also  remembered  that  the  earth  revolves  daily  from  west  to 
east,  the  cause  of  the  trade-winds  will  be  readily  understood. 

295.  The  rays  of  the  sun  as  the  earth  passes  round  be- 
neath them,  obviously  rarefy,  by  the  heat  they  impart,  the 
air  beneath,  and  the  air  so  rarefied  rises  into  the  higher 
regions  of  the  atmosphere.  While  this  takes  place,  the 
colder  air  from  the  adjoining  temperate  zones  rushes  in  to 
supply  its  place.  But  it  is  from  the  polar  regions,  north 
and  south,  that  these  colder  currents  originally  come;  and 
did  the  earth  remain  at  rest,  such  would  be  their  obvious 
direction.  Instead  of  this,  however,  north  of  the  equator 
the  direction  of  the  trade-winds  is  from  the  north-east ; 
south  of  the  equator,  from  the  south-east ; the  cause  of  _ 
which  is  thus  explained : — The  velocity  with  which  the 
surface  of  the  earth  revolves  at  the  poles,  is  inconsiderable, 
if  at  all  appreciable,  but  increases  as  we  advance,  and  is 
at  its  maximum  at  the  equator;  the  winds,  in  sweeping 
from  the  poles,  do  not  acquire  a corresponding  velocity 
with  the  motion  of  the  earth  as  they  advance  towards  the 
equator;  therefore  moving  more  slowly  than  the  earth,  they 
are  in  some  measure  left  behind,  or  appear  to  an  observer 
as  if  moving  in  a direction  contrary  to  the  rotation  of  the 
earth,  namely,  from  east  to  west.  -While  the  trade-wind 
thus  blows  upon  the  surface  of  the  earth,  there  is  no  doubt 
that  an  opposite  current,  that  of  the  rarefied  air  which  has 
ascended,  flows  towards  the  poles  at  a great  elevation  in 
the  atmosphere. 

296.  The  external  limits  of  the  trade-winds  are  39  de- 
grees north  and  30  degrees  south  of  the  equator ; but  each 
limit  diminishes  as  the  sun  advances  to  the  opposite  tropic. 
The  larger  the  expanse  of  ocean  over  which  they  sweep, 


218.  What  theory  is  stated  to  account  for  them  ? 

219.  What  of  their  limits  and  how  modified  1 


90 


PNEUMATICS. 


the  more  steadily  do  they  blow;  accordingly  they  are  more 
steady  in  the  Pacific  than  in  the  Atlantic,  and  in  the  South 
than  in  the  North  Atlantic  Ocean.  Within  the  region  of 
the  constant  trade-winds,  rain  seldom  occurs,  but  it  falls 
abundantly  in  the  adjoining  latitudes.  The  reason  is,  that 
rain  is  produced  by  the  sudden  mixture  of  air  of  ditferent 
temperatures  charged  with  moisture;  but  the  constant 
circulation  and  intermixture  of  the  air  from  the  upper 
strata  of  the  atmosphere,  or  ground  current,  maintains  so 
equal  a temperature  in  these  latitudes  as  not  to  occasion 
the  condensation  of  vapour  which  is  necessary  for  the  pro- 
duction of  rain.  Besides  which  it  is  plausibly  enough 
alleged,  that  the  aqueous  vapour  constantly  flows  off  in  the 
current  of  the  equatorial  wind  into  the  adjoining  temperate 
zones.  \\  ithin  the  limits  of  the  trade-winds,  contrary  to 
what  might  have  been  anticipated  from  the  latitude,  the 
atmosphere  is  peculiarly  cool  and  refreshing. 

SEA  AND  LAND  BREEZES. 

297.  In  most  countries  near  the  shores  of  the  sea,  but 
particularly  in  tropical  climates,  there  are  periodical  winds 
called  sea  and  land  breezes;  they  occur  in  the  following 
manner: — During  the  day,  the  wind  blows  for  a certain 
number  of  hours  from  the  sea  to  the  land  ; but  when  the 
evening  arrives,  it  changes  its  direction,  and  blows  as  many 
hours  from  the  land  to  the  sea.  In  some  countries  the  sea- 
breeze  sets  tn  about  seven  or  eight  in  the  morning,  and  is 
strongest  at  noon,  but  continues  very  sensible  until  three 
o’clock,  when  the  surfice  of  the  sea  will  be  observed  to 
exhibit  ripples  of  a deep  blue  colour.  After  this,  at  six  in 
the  evening,  the  land-breeze  commences.  The  sea  now 
assumes  a greenish  hue;  and  this  breeze  continues  until 
eio-ht  the  next  morning.  The  cause  of  this  alteration  mav 
be  readily  explained.  During  the  day,  the  air  over  the 
surface  of  the  earth  is  more  heated  bv-  the  rays  of  the  sun 
than  that  over  the  surface  of  the  sea  ; because  the  earth, 
from  its  greater  density,  comparative  state  of  rest,  d 


220.  What  of'  rain  and  the  trade-winds  ? 

221.  Explain  the  phenomena  of  sea  and  land  breezes. 


SEA  AND  LAND  BREEZES. 


fH 

numerous  elevations,  absorbs  the  sun’s  rays  sooner,  and  is 
more  heated  than  the  sea,  which,  from  its  state  of  constant 
motion  and  transparency,  imbibes  the  warmth  very  inti- 
mately, though  more  slowly.  Accordingly,  when  the  sun, 
having  risen  above  the  horizon,  has  thus  imparted  a suffi- 
cient degree  of  warmth  to  rarefy  the  body  of  air  over  the 
land,  the  air  so  rarefied  ascends  into  the  higher  regions  of 
the  atmosphere,  while  that  over  the  surface  of  the  sea, 
being  scarcely  at  all  rarefied,  rushes  in  to  supply  its  place. 
Hence,  a sea-breeze,  or  current  of  air  from  the  sea  to  the 
land,  at  this  time  prevails : but  when  the  sun  again  begins 
to  sink  below  the  horizon,  the  body  of  air  over  the  surface 
of  the  land  becomes  rapidly  cold,  because  the  earth  itself, 
by  radiation,  parts  very  quickly  with  the  warmth  it  had 
absorbed.  Then  the  land  air,  being  below  the  temperature 
of  the  sea  air,  rushes  in  to  supply  its  place,  and  thus,  during 
the  night,  a land-breeze,  or  a current  of  air  from  the  land 
to  the  sea,  is  produced. 

2 98.  When  the  sea-breeze  first  sets  in,  it  commences 
very  near  the  shore,  and  gradually  extends  itself  farther  out 
at  sea,  and,  as  the  day  advances,  becomes  more  or  less  hot. 
Hence,  the  sails  of  ships  have  been  observed  quite  becalmed 
six  or  eight  miles  out  at  sea,  while  at  the  same  time  a fresh 
sea-breeze  has  been  blowing  upon  the  shore.  The  cause 
of  this  is  obvious  ; for  it  is  natural  to  suppose  that  the  mass 
of  air  nearest  the  land  will  be  the  first  to  rush  in,  for  the 
purpose  of  supplying  the  place  of  the  air  which  is  rarefied 
immediately  above  it.  On  this  account  the  effect  of  the 
sea-breeze  is  said  not  to  be  perceptible  at  a distance  of 
more  than  five  or  six  leagues  from  the  shore,  and  for  the 
most  part  becomes  fainter  in  proportion  to  its  distance  from 
land.  The  distance,  on  the  other  hand,  to  which  the  land- 
breeze  extends  in  blowing  across  the  sea,  depends  on  the 
more  or  less  exposed  aspect  of  the  coast  from  which  it 
proceeds.  In  some  places  this  breeze  was  found  by  Dam- 
pier  brisk  three  or  four  leagues  off  shore;  in  other  places 
not  so  many  miles;  in  others,  again,  it  scarcely  extended 
without  the  rocks.  The  sea-breeze,  from  blowing  over  a 


222.  What  peculiarities  in  these  sea  breezes  T 


92 


PNEUMATICS. 


more  open  tract,  is  always  stronger  than  the  land-breeze  ; 
but  it  is  observed  that  the  land-breeze  is  much  colder  than 
the  sea-breeze.  Furthermore,  it  has  been  noticed  that  the 
tendency  of  the  land-breeze  at  night  has  almost  invariably 
a correspondence  with  the  sea-breeze  of  the  preceding  or 
following  day.  Unless  for  the  periodical  refreshing  cool 
breezes  iroin  the  sea,  the  West  India  islands,  and  generally 
all  hot  countries,  would  scarcely  be  habitable  for  the  white 
races  of  men. 

299.  The  most  dangerous  winds  to  the  navigator  are 
those  which  occur  in  sudden  gusts,  or  squalls,  and  for  the 
approach  of  which  the  sharpest  outlook  is  required.  When 
the  squall  is  in  the  form  of  a violent  tempest,  accompanied 
by  rain,  lightning,  and  thunder,  it  receives  the  name  of  a 
hurricane.  Hurricanes'  occur  most  frequently  and  with 
the  greatest  violence  in  tropical  climates,  because,  in  con- 
sequence of  the  very  great  heat  which  there  prevails,  the 
rarefaction  of  the  air,  and  also  the  condensation  of  the 
vapour  it  contains  into  rain-drops,  take  place  more  suddenly 
and  completely  than  in  more  temperate  regions.  By  this 
means  the  electricity  of  the  atmosphere — ill  it  subtle  fluid 
which  seems  to  pervade  all  bodies,  and  which  universally 
seeks  its  own  equilibrium — is  disturbed,  and  no  longer 
maintains  an  equal  distribution  through  the  aerial  vapour. 
It  accumulates  in  vast  quantities  in  one  mass  of  vapour  or 
cloud,  while  in  another  it  is  deficient;  and,  consequently, 
to  regain  its  equilibrium,  it  flashes  in  the  form  of  lightning 
from  the  surcharged  cloud,  to  the  cloud  that  is  under- 
charged, or  to  the  eartli  itself.  Hence,  hurricanes  are 
always  attended  ufith  electrical  manifestations,  which  add 
greatly  to  the  tragical  horrors  of  the  spectacle  they  exhibit. 

VENTILATION. 

300.  Ventilation  (from  Ventus.  the  Latin  word  for  wind) 
is  the  art  of  preserving  the  air  of  apartments  in  a pure  con- 
dition. 


223.  What  of  hurricanes  and  their  causes  ? 

224.  What  agency  has  electricity  in  these  ? 

225.  Define  ventilation  and  its  importance. 


VENTILATION. 


9) 


301.  This  is  an  arrangement  of  the  utmost  importance 
to  health  and  comfort.  A plentiful  supply  of  pure  air  is 
necessary  for  respiration,  because  the  air  on  being  used  by 
the  lungs  is  expelled  in  a deteriorated  condition,  and  unfit 
for  being-  again  inhaled.*  If  apartments,  therefore,  are 
not  properly  ventilated,  the  air  becomes  foul  from  the 
respired  air,  as  well  as,  perhaps,  from  impure  exhalations 
and  rarefaction  from  heat. 

302.  The  air  so  deteriorated  may  not  commonly,  produce 
immediate  death,  but  it  injures  the  health  of  those  who  live 
amongst  it,  and  is  the  fertile  cause  of  deadly  distempers, 
such  as  fevers,  cholera,  and  plague. 

303.  Besides  being  indispensable  for  breathing,  pure  air 
is  necessary  for  the  support  of  combustion.  Any  fire  de- 
prived of  a supply  of  air  languishes  and  becomes  extinguished. 
The  kind  of  air  best  adapted  for  the  supply  of  a fire  is  that 
which  is  most  pure  and  cold,  as  it  contains  more  oxygen 
in  any  given  quantity.  Oxygen  is  the  essential  element 
both  for  breathing  and  combustion  ; and  when  it  is  supplied 

* It  is  calculated  that  a man  in  ordinary  circumstances  consumes 
about  45,000  cubic  inches,  or  nearly  15,000  grains,  of  oxygen  in  twen- 
ty-four hours.  A quantity  of  carbonic  acid  gas  is  produced  in  some 
measure  proportionate  to  this  consumption.  All  the  oxygen  which  is 
inhaled  is  not  consumed;  a small  portion  returns  with  the  breath.  The 
nitrogen  of  the  air  undergoes  little  or  no  change  by  being  drawn  through 
and  expelled  from  the  lungs. 

“ In  combustion  or  burning,  it  is  [also]  the  oxygen  of  the  air  alone 
which  is  used,  the  nitrogen  remaining  unaltered.  It  is  in  consequence 
of  a chemical  attraction  subsisting  between  the  burning  body  and  the 
oxygen  of  the  air,  that  the  burning  goes  on,  the  oxygen  undergoing  a 
change  from  being  chemically  united  with  the  combustible  body,  and 
being  no  longer  able  to  support  the  combustion  of  that  substance, 
while,  at  the  same  time,  the  combustible  body  is  altered  from  being 
united  to  oxygen.  Hence  the  reason  why  a lighted  candle  is  immedi- 
ately extinguishad  if  placed  in  a quantity  of  air  from  which  the  oxygen 
has  been  withdrawn,  or  in  almost  any  situation  where  it  cannot  procure 
free  oxygen  ready  to  combine  with  the  combustible  body. 

“ Oxygen  may  be  considered  the  essential,  the  active  part  of  the  air, 
the  part  which  does  every  thing.  It  is  the  oxygen  chiefly  which  is 
engaged,  and  becomes  altered  in  all  those  chemical  operations  in  which 
the  air  is  concerned  ; the  nitrogen  seldom  undergoes  any  alteration, 
acting  chiefly  as  a damper,  moderating  the  action  of  the  oxygen,  and 
preventing  it  from  doing  too  much.” — Hugo  Reid's  Chemistry  of  Nature. 


226.  What  dangers  result  from  a want  of  it  ? 

227.  What  element  in  air  is  essential  to  combustion  ? 


94 


PNEUMATICS. 


111  a sufficient  quantity,  the  fire  burns  rapidly  and  brightly. 
The  intense  combustion  produced  by  blowing  a current  of 
air  into  a fire  by  means  of  a pair  of  bellows,  is  well  known. 
This  intense  combustion  is  produced  by  the  extraordinary 
quantity  of  oxygen  which  is  forced  into  the  burning  mass. 

3D4.  Fire  deteriorates  pure  air  as  effectually  as  breathing 
i The  oxygen  is  consumed,  and  by  a chemical  change 
m substance,  carbonic  acid  gas,  which  is  unfit  for  respira- 
tion or  combustion,  is  produced.  Fire  also  heats  and 
causes  to  expand  the  air  which  passes  unconsumed  through 
or  near  it.  This  expanded  air,  from  its  specific  lightness, 
mounts  upward,  and  endeavours  to  escape  by  any  opening 
made  for  ii  above  the  fire  place,  while  colder  and  more 
dense  air  rushes  in  to  supply  the  deficiency. 

305.  Although  carbonic  acid  gas  is  considerably  heavier 
than  pure  air  (171),  it  has  a tendency  when  heated  and 
expanded  to  mount  upward  along  with  the  air  which  has 
been  simply  heated  in  its  passage  near  the  fire.  Thus,  by 
a fortunate  provision,  all  impure  air  whatsoever  may  be 
carried  off  by  expanding  it  by  heat : in  other  words,  the 
tendency  which  a heavy  impure  air  has  to  sink,  is  overcome 
by  increase  of  temperature;  and  in  this  manner  our  warmed 
breath  and  the  warm  bad  air  from  our  fires  are  equally 
caused  to  escape  upwards,  and  leave  room  for  a fluid  suita- 
ble to  our  necessities. 

306.  Let  it  now  be  observed  that  a constant  supply  of 
air  is  necessary  in  apartments  for  two  purposes — breathing, 
and  combustion  in  the  fire  which  is  employed  for  heating 
or  cooking;  and  let  it  further  be  noted,  that  means  must 
be  provided  for  the  escape  of  the  air  after  it  has  performed 
its  office. 

307.  In  common  circumstances,  the  supply,  such  as  it  is, 
is  kept  up  by  means  of  the  occasional  opening  of  the  door, 
and  crevices  in  the  floor  and  windows;  the  whistling  of  the 
air  through  the  keyhole  and  other  small  openings,  is  an 
example  of  the  activity  of  the  atmosphere  in  rushing  to 
supply  the  internal  deficiency.  The  chimney  is  usually 
the  only  outlet. 

228.  What  analogy  between  this  and  respiration  ? 

220.  Whence  is  our  ordinary  supply  of  air,  and  how  changed  ? 


VENTILATION. 


308.  When  a fire  is  lighted  in  an  apartment.it  heats  and 
expands  a certain  quantity  of  air  near  it : the  heated  and 
expanded  air  rises : this  causes  a partial  deficiency  or 
vacuum  around  : the  air  at  a distance  rushes  to  restore  the 
equilibrium  : this  rushing  is  in  the  form  of  a current  towards 
the  fire  and  chimney,  and  is  commonly  called  draught. 

30T  The  current  of  air  so  sustained  through  an  apart- 
ment is  generally  sufficient  for  ventilation,  but  by  coming 
in  a sharp  cold  stream,  it  chills  the  person  who  is  exposed 
to  it ; and  hence  many  serious  colds,  rheumatisms,  and 
similar  affections.  Where  it  can  be  conveniently  done,  it 
is  better  to  supply  air  to  the  fire  by  a tube  direct  from  the 
atmosphere,  or  at  least  to  warm  the  air  in  a lobby,  before 
entering  the  room. 

3Kb  In  whichever  manner  air  is  supplied  to  the  fire  in 
an  apartment,  it  is  necessary  that  it  have  a passage  sufficient 
lor  entry  and  dismission.  If  .the  room  lie 
so  close  as  to  be  without  the  means  of  pas- 
sage in  and  out  lor  the  air,  the  fire  will 
speedily  heat  the  air  in  an  uniform  degree, 
like  that  in  a confined  oven,  and  ultimately 
consume  it,  when  the  fire  will  go  out. 

3!  I.  If  all  passages  into  the  apartment 
be  closed  except  the  chimney,  the  fire  will 
necessarily  supply  itself  with  fresh  air  by 
that  channel,  as  in  figure  37,  in  which  the 
heated  air  is  observed  to  be  ascending  di- 
rectly over  the  fire,  while  a stream  of  pure  and  cold  air  is 
o;i  each  side  descending  the  chimney  to  the 
fireplace  beneath.  This  process  of  ascend- 
ing and  descending  continues  as  long  as  no 
other  inlet  is  allowed  for  the  introduction 
of  air  to  the  fire. 

312.  When  a free  passage  is  left  for  the 
entrance  of  air,  and  also  a proper  outlet 
above  the  fire,  the  air  moves  rapidly  to  the 
seat  of  combustion,  passes  through  the  fire, 

. 38.  and  ascends  in  an  expanded  volume  in  the 


230.  What  of  a draught  ? 

231.  Explain  the  diagram. 


06 


PNEUMATICS. 


chimney.  A representation  of  this  process  of  supply  and 
emission  is  given  in  Figure  3S.  In  such  a case  the  chim- 
ney is  said  to  have  a good  draught  or  to  draw  well;  but 
these  terms  are  not  correct.  The  draught  is  only  the 
rushing  of  the  air  to  fill  the  partial  vacuum  over  the  fire 
and  in  the  chimney. 

313.  Such  is  the  rapid  consumption  of  fresh  air  in  a fire, 
and  the  force  with  which  a current  moves  to  supply  the  de- 
ficiency, that  air  from  the  outer  atmosphere  will  penetrate 
any  accessible  channel  to  get  to  the  seat  of  consumption. 
In  this  respect,  the  air  resembles  water  when  any  part  of 
its  volume  is  removed : the  rest  of  the  water  hastens  to  re- 
store a level  throughout  its  mass. 

314.  In  Figure  39  we  have  an  example  of  this  activity 
in  the  air,  which  represents  a closed 
apartment  with  a channel  for  intro- 
ducing fresh  air  behind  the  fire- 
place. The  air  rushes  down  this 
channel,  passes  through  the  fire, 
and  then  ascends  in  the  chimney, 
and  escapes.  In  this,  as  in  simi- 
lar cases,  the  air  shows  no  reluc- 
tance to  descend  the  channel  ; it 
indeed  is  compelled  to  do  so,  be- 
cause the  consumption  caused  by  the  fire  has  thinned  the 
air,  or  caused  a partial  emptiness  of  air  in  the  apartment, 
and  the  outer  air  being  dense,  must  sink  down  to  restore 
the  equilibrium. 

315.  Smokiness  in  an  apartment  arises  from  various 
causes,  but  in  most  cases  it  can  be  traced  to  some  impro- 
priety in  ventilation  or  malconstruction  of  chimney.  Smoke 
consists  of  exceedingly  small  particles  of  coal  or  culm,  and 
the  vapourof  bituminous  matter  and  water,  which  are  carried 
upward  along  with  the  ascending  heated  air  from  the  fire  : 
as  long  as  the  united  mass  retains  its  heat,  the  smoke  is 
seen  to  rise  in  a compact  body  from  the  top  of  the  chimney  ; 


232.  What  analogy  is  referred  to  ? 

233.  Explain  the  first  diagram. 

234.  Define  smoke  and  its  source. 


VENTILATION. 


f.7 


shortly  after  which  the  heat  is  withdrawn  by  coming  in 
contact  with  the  cool  external  atmosphere,  and  the  particles 
of  culm,  no  longer  supported,  fall  by  their  natural  gravity 
to  the  earth. 

316.  One  common  cause  of  smokiness  in  an  apartment 
is  the  want  of  a sufficient  supply  of  air  to  the  fire  by  the 
door,  windows,  or  other  lower  openings.  In  common  lan- 
guage, the  room  is  too  close.  In  this 
case  the  fire,  as  already  stated,  draws 
its  supply  from  the  chimney.  While 
the  heated  air  ascends,  a stream  of 
cold  air  descends,  as  in  Figure  40, 
and  in  its  descent  it  entangles  the 
heated  air  loaded  with  smoke,  and 
so  brings  down  along  with  it  a por- 
tion of  the  smoke  into  the  apartment. 

Fig.  40.  An  additional  and  properly  situated 

opening  in  the  room,  will  generally  remove  this  cause  of 
smokiness. 

317.  Another  common  cause  of  smokiness  is  too  great  a 
width  of  chimney,  particularly  beneath  or  near  the  fireplace. 
If  the  chimney  be  too  wide  throughout  its  length,  the  volume 
of  heated  air  from  the  fire  is  insufficient  to  fill  it;  conse- 
quently it  mounts  sluggishly,  is  entangled  with  cold  air  en- 
tering both  from  above  and  beneath,  and  so  partially  returns, 
on  the  occurrence  of  winds,  into  the  room  It  is  important 
for  riddance  of  smoke  that  the  chimney  should  contain  only 
a heated  column  of  air,  which  has  a tendency  to  shoot 
rapidly  upwards  and  escape.  The  longer  such  a column 
is  (that  is,  the  taller  the  chimney),  the  more  difficult  is  it 
for  the  cold  air  above  to  retard  its  emission. 

318.  The  most  common  cause  o smokiness  is  the  im- 
proper construction  of  the  fireplace  and  lower  part  of  the 
chimney.  These  are  made  so  wideband  open  that  cold  air 
rushes  into  the  chimney  from  the  room  without  passing 
through  or  near  the  fire.  This  cold  or  heavy  air  mingles 


235.  Explain  the  next  diagram. 

236.  What  other  cause  of  smokiness  is  named  ? 

237.  Name  the  most  common  cause. 


98 


PNEUMATICS. 


with  the  heated  smoky  air,  cools  it,  and  brings  back  a por- 
tion of  it  into  the  room,  in  which  the  air  is  less  dense  than 
the  external  air.  The  remedy  for  this  consists  in  narrow- 
ing the  fireplace  and  throat  of  the  chimney,  so  that  all  air 
shall  first  be  heated  before  it  commences  its  ascent.  By 
doing  so,  the  tendency  in  the  heated  air  to  rise  completely 
overcomes  the  falling  tendency  in  the  particles  of  culm. 

319.  Smoke  sometimes  descends  a chimney  into  a room 
from  an  adjacent  chimney  top,  in  which  case  it  is  usually 
called  back  smoke.  This  happens  when  the  chimney  and 
room  contain  air  specifically  lighter  than  the  external  at- 
mosphere, and  no  inlet  is  allowed  to  restore  the  balance 
except  the  chimney.  The  air  in  the  chimney  cools  and 
sinks,  carrying  an  odour  of  soot  with  it  into  the  room ; and 
this  being  still  insufficient  to  restore  the  equilibrium,  a cer- 
tain portion  of  atmospheric  air  also  descends,  bringing  with 
it  the  smoke  of  the  next  house.  If  a room  be  left  with  an 
open  chimney  in  summer,  such  a phenomenon  is  certain  to 
occur.  The  air  being  warmer  or  more  light  outside  during 
the  day,  the  air  of  the  room  rushes  up  the  chimney,  leaving 
a partial  emptiness;  and  at  night  there  is  a reverse  motion, 
which  brings  the  odour  of  soot,  or  perhaps  smoke,  along 
with  it. 

320.  Smokiness  may  occur  from  the  peculiar  situation 
of  a house,' as  for  instance  in  a low  dwelling  near  a tall  pile 
o ' building,  over  which  the  wind  is  apt  to  gush  with  rapidity 
into  the  low  chimney,  as  water  falls  over  a precipice,  and 
so  overcoming  all  obstacles  before  it.  But  in  by  far  the 
greater  number  of  cases,  the  smokiness  is  dependent  on 
those  circumstances  above  mentioned,  and  might  be  en- 
tirely remedied  by  proper  attention  to  a few  simple  rules  in 
pneumatics.  It  must  always  be  borne  in  mind  that  the 
cause  of  the  smoke  is  something  connected  with  the  air ; 
the  smoke  itself  acting  only  a secondary  part  in  the  phe- 
nomenon. 

321.  Large  apartments,  such  as  churches,  halls  of  public 
assembly,  and  schools,  in  which  there  is  a large  consump- 


238.  What  of  smoke  from  the  next  house  1 

239.  What  of  the  relative  situation  of  houses  1 


VENTILATION. 


9J 


tioii  of  air  by  respiration,  require  to  be  ventilated  in  a par- 
ticular manner.  The  chimney,  if  they  have  one,  is  incom- 
petent to  carry  off  the  foul  air;  and  if  they  have  no  such 
outlet,  the  case  becomes  the  more  urgent.  In  many 
instances,  the  only  means  of  ventilation  which  are  em- 
ployed is  to  let  down  the  upper  sashes  of  the  windows; 
but  this  is  a very  clumsy  mode  of  procedure,  and  may  have 
dangerous  effects  from  the  currents  of  cold  air  which  rusii 
into  the  room.  Besides,  the  plan  is  inefficacious  in  war  n 
weather,  when  ventilation  is  most  required,  because  the  air 
outside  being  at  the  same  temperature  as  that  inside,  there 
will  be  no  rush  either  way : the  whole  will  be  in  a state 
of  stagnation. 

322.  To  ventilate  properly  in  these  cases,  the  equilibrium 
of  the  air  must  be  destroyed,  in  order  to  cause  the  foul  air 
in  the  apartment  to  rush  away  to  restore  the  atmospheric 
balance,  and  in  doing  so  leave  the  room  to  be  filled  with 
fresh  air.  To  accomplish  this  sure  method  of  ventilation, 
the  floor  or  some  other  lower  part  of  the  room  must  be 
perforated  with  innumerable  small  holes,  through  which 
currents  of  fresh  air  will  be  introduced  from  the  exterior 
of  the  building.  The  ceiling  must  be  similarly  perforated 


240.  What  oflarge  apartments  ? 

241.  Explain  the  diagram. 


rjo 


PNEUMATICS. 


with  holes  to  carry  off  the  ascending  streams  of  breathed 
warm  air.  From  above  the  ceiling,  the  air  is  carried  along 
and  down  a channel  to  a fire,  which  highly  rarefies  it,  and 
shoots  it  up  a chimney  along  with  the  smoke  from  the  fire. 
A representation  of  this  method  of  ventilation,  which  is  a 
device  of  the  eminent  chemist  Dr.  D.  B.  Reid,  is  given  in 
Figure  41.  The  air  enters  by  a channel  a b r,  thence  ascends 
into  the  room,  passes  off  at  the  ceiling,  and  is  conveyed  to 
the  fire  k,  after  which  it  ascends  into  the  atmosphere.  Valves 
or  dampers  may  be  placed  in  the  channels  to  regulate  the 
admission  and  emission  of  the  air. 

323.  By  thus  establishing  a fire  somewhere  adjacent, 
and  opening  a communication  to  it  from  an  apartment,  any 
kind  of  foul  air  may  be  effectually  drawn  off.  On  the  same 
principle,  a deep  vat  or  pit  containing  carbonic  acid  gas, 
or  any  other  air  specifically  heavier  than  the  atmosphere, 
may  be  drained  of  its  contents  by  plunging  the  lower  ex- 
tremity of  a tube  into  it,  and  directing  the  other  end  to  a fire. 
The  fire  will  thus  draw  a portion  of  its  supply  of  air  from 
the  pit,  and  so  carry  oft’  the  deletorious  vapour. 

324.  When  it  would  be  inconvenient  to  ventilate  by 
means  of  a fire,  force  may  be  employed  to  propel  pure  air 
into  a confined  apartment.  We  have  an  example  of  this 
in  the  case  of  the  diving-bell. 

THE  DIVING-BELL. 

325.  The  diving-bell  is  an  iron  box  or  apartment  let 
down  into  water,  and  containing  two  or  more  men  who 
are  to  be  employed  in  some  kind  of  mechanical  operation 
at  the  bottom.  It  is  chiefly  used  in  building  the  founda- 
tions of  piers  in  the  sea,  at  a depth  of  from  twelve  to  twenty 
feet  below  the  surface,  and  in  gathering  at  a much  greater 
depth  the  valuable  relics  of  vessels  which  have  been  wrecked 
and  sunk. 

326.  Originally,  the  machine  resembled  a bell  in  figure  ; 
it  is  now  generally  shaped  like  a square  box,  narrower  at 
the  top  than  the  bottom.  It  is  made  of  iron,  is  perfectly 


242.  Describe  the  use  of  a fire  for  ventilation. 

243.  Define  a diving-bell  and  its  use. 


THE  DIVING-BELL. 


101 


cl  >se  except  in  the  bottom  or  mouth,  which  is  open,  and  is 
suspend  d by  a strong  chain  from  a crane  on  the  deck  of 
a vessel.  It  is  from  six  to  eight  feet  in  height,  with  two  or 
more  glass  lenses  on  the  top  to  admit  light  from  above 
when  it  is  sunk,  and  there  is  a sent  round  the  interior  for 
the  accommodation  of  those  who  descend. 

327.  Figure  42  is  an  outline  representation  of  a diving-bell 

r T C and  its  apparatus.  B is  the 

bell  containing  two  men, 
one  on  the  seat,  and  the 
other  in  the  act  of  tying  a 
rope  R to  a prostrate  can- 
non, which,  on  giving  a 
preconcerted  signal,  will 
be  hauled  up  to  a vessel 
on  the  surface  of  the  water. 
C is  the  chain  by  which 
the  bell  is  suspended,  and 
T is  a flexible  leather  tube 
by  which  fresh  air  is  ad- 
mitted into  the  bell.  There 
is  a stopcock  on  the  mouth 
of  the  tube,  by  which  the 
Fig-  42.  men  can  regulate  the  ad- 

mission of  air  at  pleasure.  The  bell  does  not  touch  the 
bottom,  but  hangs  within  a few  inches  or  perhaps  one  or 
two  fcet  of  it,  and  therefore  the  men  are  provided  with  long 
leather  boots,  to  protect  them  while  they  stand  upon  the 
bottom  in  the  water. 

328.  Tiie  manner  in  which  the  diving  bell  is  supplied 
with  fresh  air,  and  freed  from  that  which  is  impure,  is  most 
deserving  of  our  attention. 

329.  When  the  bell  is  lowered,  so  as  to  touch  and  sink 
beneath  the  surface  of  the  sea,  it  may  be  compared  to  the 
dipping  of  a tumbler,  mouth  downwards,  in  a vessel  of 
water.  In  the  same  manner  as  the  air  within  the  tumbler 
keeps  the  liquid  from  filling  it,  so  does  the  air  within  the 


244.  Explain  the  diagram. 

245.  How  is  a diving-bell  supplied  with  air  ? 


102 


PNEUMATICS. 


bell  prevent  the  water  from  rising  beyond  a certain  height. 
As  the  bell  sinks,  the  air  which  it  contains  becomes  gra- 
dually more  compressed  in  bulk  by  the  intrusion  of  water, 
and  at  a depth  of  thirty-four  feet,  the  air  is  condensed  into 
one-half  of  its  natural  dimensions.  At  this  point,  therefore, 
if  no  precautions  were  used,  the  bell  would  be  half-filled 
with  water.  The  means  adopted  to  keep  the  water  out 
consists  in  forcing  in  air  through  the  already  mentioned 
tube.  On  the  deck  of  the  superintending  vessel  is  placed 
a powerful  air  cendensing-pump,  wrought  by  one  or  two 
men  inconstant  attendance;  and  by  this  machine  fresh 
air  is  injected  into  the  bell,  and  kept  at  such  a density  as 
forces  the  water  entirely  out,  or  very  nearly  so. 

330.  The  bell  is  freed  of  impure  air  by.  means  of  a sep- 
arate tube  and  stopcock,  fixed  in  its  upper  part;  but  in 
some  cases  such  an  arrangement  is  not  considered  neces- 
sary, as  the  expired  air  on  becoming  cool,  and  consisting 
chiefly  of  carbonic  acid  gas,  descends  by  its  greater  weight 
to  the  bottom,  and  escapes  round  the  low:er  edges  of  the 
bell,  whence  it  rises  in  bubbles  to  the  surface. 

PNEU  I ATICS— CONCLUDED. 

BUOYANT  PROPERTY  OF  AERIFORM  FLUIDS. 

331.  The  atmosphere,  as  has  been  stated,  possesses  the 
property  of  buoying  up  bodies  which,  bulk  for  bulk,  are 
lighter  than  itself.  The  law  governing  bouyancy  in  liquids 
is  precisely  the  same  as  that  governing  bouyancy  in  aeri- 
form fluids,  and  may  here  be  repeated  in  reference  to  air. 

332.  First. — Any  solid  body  immersed  in  a fluid  dis- 
places exactly  its  own  bulk  of  fluid,  and  the  force  with 
which  the  body  is  buoyed  up  is  equal  to  the  weight  of  the 
fluid  which  is  displaced.  This  refers  to  bodies  of  less 
density  than  air. 

333.  Second. — Any  solid  body  of  a greater  density  than 
air,  when  w'holly  immersed  in  that  fluid,  loses  exactly  as 

246.  How  is  impure  air  removed  ? 

247. -  What  of  the  buoyancy  of  air  ? 

24S.  What  analogy  between  air  and  water  t 


BUOYANT  PROPERTY  OF  AERIFORM  FLUIDS.  1 13 

much  of  its  weight  as  the  weight  of  ail  equal  bulk  of  air — 
tic: t is,  i f she  air  which  it  displaces. 

As  these  propositions  have  been  sufficiently  exemplified 
in  a preceding  part  of  the  present  work,  from  paragraph  83 
to  108,  and  as  the  fluid  support  of  air  is  in  principle  the 
same  as  that  of  water,  little  additional  explanation  is  here 
required  upon  the  subject. 

334.  The  support  afforded  to  bodies  in  the  atmospheric 
fluid  by  its  resistance  is  very  evident  from  • many  appear- 
ances in  nature,  as  the  support  of  vapours  or  clouds,  the 
rising  of  smoke  and  fine  particles  of  dust,  and  the  flying  of 
birds ; in  art,  it  is  exemplified  by  the  flying  of  a boy’s  paper 
kite,  the  rising  of  soap-bubbles,  and  its  buoyant,  property 
by  the  floating  of  balloons. 

335.  The  flight  of  birds  is  not  accomplished  altogether 
by  the  buoyant  property  in  the  air.  These  animals  support 
themselves  by  striking  their  wings  against  the  fluid  through 
which  they  are  passing,  and  this  friction,  along  with  the 
property  of  buoyancy  in  the  atmosphere,  sustains  them  at 
any  height  to  which  they  are  pleased  to  ascend.  Birds  do 
not  generally  fly  above  half  a mile  in  height,  and  seldom 
above  a few  hundred  yards.  At  considerable  elevations 
the  air  is  so  specifically  light,  as  to  be  unsuitable  for  their 
easy  support.  Those  which  rise  to  the  higher  regions  of 
the  atmosphere,  as  for  instance  the  eagle,  are  provided  with 
large  wings,  which  enahle  them  to  support  themselves  in 
the  comparatively  thin  fluid  in  which  they  move.  A small 
bird,  when  let  out  from  a balloon,  at  the  height  of  three 
miles,  drops  almost  like  a plummet,  till  it  arrive  in  a fluid 
against  which  its  little  wings  can  take  effect. 

336.  The  buoyant  property  of  the  air  thus  obviously 
diminishes  in  proportion  as  it  becomes  less  dense ; and 
there  is  a point  above  which  the  lightest  imaginable  body 
or  particle  of  matter  would  inevitably  sink.  By  this  means, 
independently  of  terrestrial  attraction,  an  effectual  limit  has 


249.  What  examples  of  buoyancy  are  named  1 

250.  What  of  the  flight  of  birds  ? 

251.  What  of  the  higher  regions  of  the  air  1 


104 


PNEUMATICS. 


been  set  to  the  distance  attainable  by  substances  from  the 
surface  of  our  planet.  Not  an  atom  of  matter,  since  the 
period  of  the  creation,  has  been  suffered  to  escape  beyond 
the  higher  regions  of  the  atmosphere,  or  which  has  not  in 
making  the  attempt  been  brought  back  to  the  earth. 

337.  The  support  given  to  bodies  by  the  atmosphere 
diminishes  their  apparent  weight,  in  the  same  manner  as 
the  apparent  weight  of  bodies  is  diminished  in  water.  A 
stone  is  moved  more  easily  in  water  than  in  air,  and  so 
likewise  is  it  moved  more  easily  in  air  than  in  a vacuum. 

338.  The  diminution  in  weight  of  a body  in  air,.a3 
already  stated  (334),  is  equal  to  the  weight  of  the  bulk  of 
air  displaced.  Thus,  if  an  object  which  displaces  one  grain 
of  air,  weigh  a pound  in  a vacuum,  it  will  weigh  one  grain 
less  than  a pound  in  air,  and  therefore  one  gr  in  will  require 
to  be  added  to  it  to  make  up  the  apparent  deficiency. 

339.  The  weight  of  air  displaced  by  any  merchantable 
object  is  so  exceedingly  trifling  as  not  to  be  worth  reckon 
ing  in  ordinary  circumstances.  Strictly  speaking,  however, 
that  weight  of  air  has  an  influence  in  the  value  of  the  trans- 
action. In  all  cases  in  which  the  object  weighed  is  more 
bulky  than  the  weight  employed  to  balance  it,  a certain 
quantity  must  be  added  to  overcome  the  force  with  which 
it  is  buoyed  up  by  the  atmospheric  fluid. 

340.  A pound  of  leathers  lightly  piled  together  contains 
somewhat  more  weight  than  a pound  of  lead.  We  may 
prove  that  such  is  the  case,  by  taking  the  apparent  pound 
of  feathers  and  forcing  them  into  a small  bulk  in  an  air- 
tight covering,  and  then  weighing  them  again,  when  it  will 
be  perceived  that  they  will  weigh  a little  more  than  a pound. 
In  strict  justice  to  seller  and  buyer,  all  commodities  should 
either  be  weighed  in  vacuo,  or  balanced  against  weights  of 
equal  bulk. 

BALLOONS. 

3»1.  The  light  heated  air  which  escapes  from  a fire, 
ascends,  and  is  buoyed  up  by  the  more  dense  air  beneath. 


252.  What  of  the  weight  of  air,  and  the  illustrations  ? 

253.  Explain  the  principle  of  balloons. 


balloons. 


105 


Hydrogen  or  any  other  gas  of  a less  specific  gravity  than 
air,  in  the  same  manner  ascends  and  floats  in  the  atmo- 
sphere at  the  height  at  which  it  finds  air  of  its  own  specific 
gravity. 

342.  On  the  same  principle,  if  heated  air  or  any  light 
gas  be  inclosed  in  a large  silk  bag,  it  will  ascend  in  the 
atmosphere  till  it  reach  a region  of  air  which  is  incapable 
of  supporting  it.  Thus,  a soap-bubble  inclosing  warm  air 
readily  ascends  to  the  ceiling  of  an  apartment.  If  the  bub- 
ble be  made  with  cold  water,  it  will  sink  instead  of  rising. 

343.  A balloon  is  a bag  made  of  fine  varnished  silk,  and 
of  such  a magnitude  that  the  difference  betwixt  the  weight 
of  its  contents  and  that  of  the  displaced  air  is  sufficient  to 
support  the  weight  of  the  silk  and  the  other  parts  of  the 
apparatus. 

344.  Balloons  were  originally  made  to  rise  by  being 
filled  with  heated  air  from  a fire  hung  beneath  them ; but 
this  dangerous  and  inconvenient  practice  was  in  course  of 
time  superseded  by  the  use  of  hydrogen  gas,  one  of  the 
lightest  airs  which  can  be  prepared.  Hydrogen  gas  has 
latterly  been  succeeded  by  carburetted  hydrogen,  which 
though  not  so  light,  is  more  easily  obtained,  being  the  gas 
with  which  towns  are  now  generally  lighted. 

345.  Employing  a moderately  pure  and  light  gas,  the 
contents  of  a balloon  may  be  estimated  to  weigh  only  an 
eighth  of  the  weight  of  the  atmosphere,  bulk  for  bulk  ; and 
hence,  after  adding  another  eighth  for  weight  of  apparatus, 
it  will  ascend  with  a force  of  six-eighths;  in  other  words, 
if  the  gas  and  apparatus  weigh  two  pounds,  the  balloon  will 
lift  from  the  ground  a weight  of  other  six  pounds. 

346.  The  force  with  which  a balloon  will  ascend  is  there- 
fore to  be  calculated  by  measuring  its  capacity  in  cubic 
feet,  and  comparing  the  result  with  an  equal  bulk  of  ainm- 
spheric  air:  the  difference  of  weight  is  the  buoyant  fi'rce 
of  the  balloon 


254.  How  were  they  formerly  made  to  rise  ? 

255.  What  ^as  is  now  employed,  and  why  ? 

256.  How  is  its  force  of  ascent  calculated  ? 


106 


PNEUMATICS. 


347.  Of  aerostation,  or  the  art  of  moving  through  the 
air  in  balloons, great  expectations  were  originally  entertain- 
ed, but  the  experience  of  half  a century  has  proved  that  it 
is  of  no  practical  value.  Its  only  use  is  the  exhibition  of 
an  interesting  principle  in  pneumatics.  A balloon  con- 
structed in  the  best  known  manner,  and  moving  upwards 
with  a powerful  force,  is  subject  to  the  following  draw- 
backs : — 

348.  As  the  balloon  ascends,  its  contents  expand  in  con- 
sequence of  the  increasing  rarefaction  of  the  atmosphere; 
if,  therefore,  it  has  been  entirely  filled  when  on  the  ground, 
a portion  of  the  gas  must  be  allowed  to  escape  as  it  rises, 
otherwise  it  will  burst.  At  the  height  of  3000  feet,  the 
atmosphere  is  a tenth  degree  less  dense  than  on  the  surface 
of -the  earth;  hence  the  gas  expands  a tenth  in  bulk,  and  a 
tenth  must  be  suffered  to  escape.  This  amounts  to  8000 
feet  of  gas  in  a balloon  containing  80,000  feet;  calculating 
the  gas  at  36  lbs.  per  1000  cubic  feet,  the  loss  incurred  by 
the  escape  at  this  limited  height  would  be  equal  to  288  lbs. 
of  buoyant  power.  As  the  atmosphere  becomes  the  more 
rare  as  the  machine  ascends,  the  expansion  proceeds,  more 
gas  must  be  emitted,  and  more  buoyant  power  lost. 

349.  Again,  at  the  approach  of  night,  upon  the  passage 
through  clouds,  or  under  the  influence  of  a shower  of  rain, 
a large  quantity  of  moisture  becomes  absorbed  by  the  net 
which  encloses  the  balloon  and  other  apparatus,  frequentlv 
to  the  extent  of  two  or  three  hundred-weight,  requiring  an 
immediate  discharge  of  ballast  to  that  amount,  to  prevent 
the  balloon  from  being  borne  to  the  ground.  As  the  morn- 
ing approaches,  or  the  influence  of  increasing  heat  begins 
to  be  felt,  the  moisture  becomes  dissipated  ; and  there  being 
no  means  of  recovering  the  lost  ballast,  the  balloon  rapidly 
rises  in  the  air,  its  contents  expanding  in  the  ascent,  and 
rendering  further  liberations  of  gas  necessary  to  prevent 
explosion.  These  alternations  continuing  to  operate  more 
or  less  frequently,  it  is  evident  that  they  must  soon  put  an 
end  to  the  buoyant  pow'er,  however  great  originally,  and 


257.  What  disadvantages  attend  upon  balloons  ? 


BALLOONS. 


107 


forcibly  terminate  the  excursion  through  the  air.  Such  are 
the  principal  causes  which  affect  the  continuance  of  aerial 
voyages  for  any  length  of  time,  and  along  with  the  contend- 
ing eifects  of  winds,  against  which  there  can  be  no  pre- 
ventive, render  aerostation  only  a matter  of  amusement  to 
a public  assemblage. 


DAVIES’  SYSTEM  OF  MATHEMATICS. 


MAMEMMETCAlt  W©iM: 

DESIGNED  FOR  SCHOOLS,  ACADEMIES,  AND  COLLEGES. 

BY  CHARLES  DAVIES,  LL.D. 


PUBLISHED  BY  A.  S.  BARNES  & CO.. 

51  JOHN-STREET,  NEW  YORK. 


ELEMENTARY  COURSE. 


Pnea 

UAVTES’  PRIMARY  TABLE  BOOK IS 

DAVIES’  FIRST  LESSONS  IN  ARITHMETIC ......'  18 

DAVIES’  SCHOOL  ARITHMETIC  Ncu>  Edition,  38 

KEY  TO  DAVIES’  SCHOOL  ARITHMETIC 38 

DAVIES’  UNIVERSITY  ARITHMETIC 12mo.  aheep,  75 

KEY  TO^DAVIES’  UNIVERSITY  ARITHMETIC 50 

DAVIES’  ELEMENTARY  ALGEBRA 12mo.  aheep,  84 

KEY  TO  DAVIES’  ELEMENTARY  ALGEBRA 50 

DAVIES’  ELEMENTARY  GEOMETRY I2mo.  aheep,  75 

DAVIES’  DRAWING  AND  MENSURATION 12mo.  sheep,  84 


ADVANCED  COURSE. 

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cing the  Rectification  and  Quadrature  of  Curves,  the  Mensuration  of 
Surfaces,  and  the  Cubature  of  Solids 8no.  sheep.  1 50 

DAVIES’  DESCRIPTIVE  GEOMETRY— With  its  application  to  Spheri- 
cal Projections s.  n.  sheep,  2 08 

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VV,tb  numerous  Plates bvo  calf  back,  2 54 

(a) 


Davies’  System  of  Mathematics. 


TO  THE  FRIENDS  OF  EDUCATION. 

The  publishers  of  this  series  of  mathematical  works  by  Professor 
Chahi.es  Davies,  heir  leave  respectfully  to  ask  of  teachers  and  the 
friends  of  education  a careful  examination  of  these  works.  It  is 
not  their  intention  to  commend,  particularly,  this  Course  of  Math- 
ematics to  public  favor ; and  especially,  it  is  not  their  design  to 
disparage  other  works  on  the  same  subjects.  They  wish  simply 
to  explain  the  leading  features  of  this  system  of  Text-Books — the 
place  which  each  is  intended  to  fill  in  a system  of  education — the 
general  connection  of  the  books  with  each  other — and  some  of  the 
advantages  which  result  from  the  study  of  a uniform  series  of  math- 
ematical works. 

It  may,  perhaps,  not  be  out  of  place,  first,  to  remark,  that  the 
author  of  this  series,  after  graduating  at  the  Military  Academy, 
entered  upon  the  duties  of  a permanent  instructor  in  that  institution 
in  the  year  1816,  and  was  employed  for  the  twenty  following  years 
in  the  departments  of  scientific  instruction.  At  the  expiration  of 
that  period  he  visited  Europe,  and  had  a full  opportunity  of  com- 
paring the  systems  of  scientific  instruction,  both  in  F^.nce  and 
England,  with  that  which  had  been  previously  adopted  at  the  Mili- 
tary Academy. 

This  series,  combining  all  that  is  most  valuable  in  the  various 
methods  of  European  instruction,  improved  and  matured  by  the 
suggestions  of  more  than  thirty  years’  experience,  now  forms  the 
only  complete  consecutive  course  of  Mathematics.  Its  methods, 
harmonizing  as  the  works  of  one  mind,  carry  the  student  onward 
by  the  same  analogies  and  the  same  law's  of  association,  and  are  cal- 
culated to  impart  a comprehensive  knowledge  of  the  science,  com- 
bining clearness  in  the  several  branches,  and  unity  and  proportion 
in  the  whole.  Being  the  system  so  long  in  use  at  West  Point,  and 
through  which  so  many  men,  eminent  for  their  scientific  attain- 
ments, have  passed,  it  may  be  justly  regarded  as  our  National 
System  of  Mathematics.  Scholars  and  students  who  have  pur- 
sued this  course,  w'ill  everywhere  stand  on  the  highest  level  with 
reference  to  the  estimates  which  themselves  and  others  will  form 
of  this  part  of  their  education. 

The  series  is  divided  into  three  parts,  viz.  : First — Arithmeti- 
cal Course  for  Schools.  Second — Academical  Course.  Turd 
—Collegiate  Course. 


(3) 


Davies'  System  if  Mathematics. 


The  Arithmetical  Course  for  Schools. 

I.  PRIMARY  TABLE-BOOK. 

II.  FIRST  LESSONS  IN  ARITHMETIC. 

III.  SCHOOL  ARITHMETIC.  (Key  separated 


PRIMARY  TABLE-BOOK. 

The  leading  feature  of  the  plan  of  this  work  is  to  teach  the  reading  of  figures 
that  is,  so  to  train  the  mind  that  it  shall,  by  the  aid  of  the  eye  alone,  catch  in 
stantly  the  idea  which  any  combination  of  figures  is  intended  to  express. 

The  method  heretofore  pursued  has  aimed  only  at  presenting  the  combinations 
by  means  of  our  common  language  : this  method  proposes  to  present  them  pure- 
ly through  the  arithmetical  symbols,  so  that  the  pupil  shall  not  be  obliged  to  pause 
at  every  step  and  translate  his  conceptions  into  common  language,  and  then  re- 
translate them  into  the  language  of  arithmetic. 

For  example,  when  he  sees  two  numbers,  as  4 and  8,  to  be  added,  he  shall  not 
pause  and  say,  4 and  8 are  12,  but  shall  be  so  trained  as  to  repeat  12  at  once,  as  is 
always  done  by  an  experienced  accountant.  So  if  the  difference  of  these  num- 
bers is  to  be  found,  he  shall  at  once  say  4,  and  not  4 from  8 leaves  4.  If  he  de- 
sires their  product,  he  will  say  32  , if  their  quotient,  2 : and  the  same  in  all  simi- 
lar cases. 


FIRST  LESSONS  IN  ARITHMETIC. 

The  First  Lessons  in  Jliilhmetic  begin  with  counting,  and  advance  step  by  step 
through  all  the  simple  combinations  of  numbers.  In  order  that  the  pupil  may  be 
impressed  with  the  fact  that  numbers  express  a collection  of  units,  or  things  of 
the  same  kind,  the  unit,  in  the  beginning,  is  represented  by  a star,  and  the  child 
should  be  made  to  count  the  stars  in  all  cases  where  they  are  used  Having  once 
fixed  in  the  mind  a correct  impression  of  numbers,  it  was  deemed  no  longer 
necessary  to  represent  the  unit  by  a symbol ; and  hence  the  use  of  the  star  was 
discontinued.  In  adding  1 to  each  number  from  1 to  10,  we  have  the  first  ten 
combinations  in  arithmetic.  Then  by  adding  2 in  the  same  way,  we  have  the 
second  ten  combinations,  and  so  on.  Each  ten  combinations  is  arranged  in  a 
separate  lesson,  throughout, the  four  ground  rules,  and  each  is  illustrated  either 
by  unit  marks  or  a simple  example.  Thus  the  four  hundred  elementary  combi- 
nations are  presented,  in  succession,  in  forty  lessons, — a plan  not  adopted  in  any 
other  elementary  book. 

SCHOOL  ARITHMETIC. 

This  work  begins  with  the  simplest  combination  of  numbers,  and  contains  all 
that  is  supposed  to  be  necessary  for  the  average  grade  of  classes  in  schools.  It 
is  strictly  scientific  and  entirely  practical  in  its  plan  Each  idea  is  first  presented 
to  the  mind  either  by  an  example  or  an  illustration,  and  then  the  principle,  or 
abstract  idea,  is  stated  in  general  terms.  Great  care  has  been  taken  to  attain 
simplicity  and  accuracy  in  the  definitions  and  rules  and  at  the  same  time  so  to 
frame  them  as  to  make  them  introductory  to  the  higher  branches  of  mathematica. 
science.  No  definition  or  rule  is  given  until  the  mind  of  the  pupil  has  been 
brought  to  it  by  a series  of  simple  inductions,  so  that  mental  training  may  begin 
wnh  the  first  intellectual  efforts  in  numbers 


4 


Danes ’ System  of  Mathematics. 


The  Academic  Course. 

I.  THE  UNIVERSITY  ARITHMETIC.  (Key  separate.) 

II.  PRACTICAL  GEOMETRY  AND  MENSURATION. 

III.  ELEMENTARY  ALGEBRA.  (Key separate,) 

IV.  ELEMENTARY  GEOMETRY. 

V.  DAVIES’  ELEMENTS  OF  SURVEYING. 

Those  who  are  conversant  with  the  preparation  of  elementary 
text-hooks,  have  experienced  the  difficulty  of  adapting  them  to  the 
wants  which  they  are  intended  to  supply.  The  institutions  of  in- 
struction are  of  all  grades  from  the  college  to  the  district  school, 
and  although  there  is  a wide  difference  between  the  extremes,  the 
level  in  passing  from  one  grade  to  the  other  is  scarcely  broken. 
Each  of  these  classes  of  seminaries  requires  text-books  adapted  to 
its  own  peculiar  wants  ; and  if  each  held  its  proper  place  in -its 
own  class,  the  task  of  supplying  suitable  text-books  would  not  be 
so  difficult.  An  indifferent  college  is  generally  inferior,  in  the 
system  and  scope  of  instruction,  to  a good  academy  or  high-school ; 
while  the  district-school  is  often  found  to  be  superior  to  its  neigh- 
boring academy. 

Although,  therefore,  the  University  Arithmetic  and  the  Practical 
Geometry  and  Mensuration,  have  been  classed  among  the  books 
appropriate  for  academies,  they  may  no  doubt  be  often  advantage- 
ously studied  in  the  common-school ; so  also  with  the  Algebra  and 
Elementary  Geometry.  The  Practical  Geometry  and  Mensura- 
tion, containing  so  much  practical  matter,  can  hardly  fail  to  be  a 
useful  and  profitable  study. 

DAVIES’  UNIVERSITY  ARITHMETIC. 

The  scholar  in  commencing  this  work,  is  supposed  to  be  familiar  with  the  oper 
ations  in  the  four  ground  rules,  which  are  fully  taught  both  in  the  First  Lessons 
and  in  the  School  Arithmetic.  This  being  premised,  the  language  of  figures, 
which  are  the  representatives  of  numbers,  is  carefully  taught,  and  the  different 
significations  of  which  the  figures  are  susceptible,  depending  on  the  places  in 
which  they  are  written,  are  fully  explained.  It  is  shown,  for  example,  that  the 
simple  numbers  in  which  the  unit  increases  from  right  to  left  according  to  the 
scale  of  tens,  and  the  Denominate  or  Compound  Numbers,  in  which  it  increases 
according  to  a different  scale,  belong  in  fact  to  the  same  class  of  numbers,  and 
that  both  may  be  treated  under  a common  set  of  rules.  Hence,  the  rules  for  No- 
tation, Addition,  Subtraction,  Multiplication,  and  Division,  have  been  so  con- 
structed as  to  apply  equally  to  all  numbers.  This  arrangement  is  a new  one,  and 
is  deemed  an  essential  improvement  in  the  science  of  numbers 

l.i  developing  the  properties  of  numbers,  from  their  elementary  to  their  highest 
combinations,  great  labor  has  been  bestowed  on  classification  and  arrangement. 
It  has  been  a leading  object  to  present  the  entire  subject  of  arithmetic  as  forming 


Dueled  System  of  Mathematics. 


a series  of  dependent  and  connected  propositions  ; so  that  the  pupil,  while  ac- 
quiring useful  and  practical  knowledge,  may  at  the  same  time  be  introduced  to 
those  beautiful  methods  of  exact  reasoning  which  science  alone  can  teach. 

Great  care  has  been  taken  to  demonstrate  fully  all  the  rules,  and  to  explain  the 
reason  of  every  process,  from  the  most  simple  to  the  most  difficult.  The  demon- 
stration of  the  rule  for  the  division  of  fractions,  on  page  147,  is  new  and  consid- 
ered valuable. 

The  properties  of  the  9’s,  explained  at  page  93,  and  the  demonstration  of  the 
four  ground  rules  by  means  of  those  properties,  are  new  in  their  present  form, 
and  are  thought  worthy  of  special  attention. 

In  the  preparation  of  the  work,  another  object  has  been  kept  constantly  in 
view  ; viz.,  to  adapt  it  to  the  business  wants  of  the  country.  For  this  purpose, 
much  pains  nave  been  bestowed  in  the  preparation  of  the  articles  on  Weights 
and  Measures,  foreign  and  domestic — on  Banking,  Bank  Discount,  Interest,  Coins 
and  Currency,  Exchanges,  Book-keeping,  &c.  In  short,  it  is  a full  treatise  on 
the  subject  of  Arithmetic,  combining  the  two  characteristics  of  a scientific  and 
practical  work. 


Recommendation  from  the  Prof es. tors  of  the  Mathematical  Department  of  the 
United  States  Military  Academy 

In  the  distinctness  with  which  the  various  definitions  are  given— the  clear  and 
strictly  mathematical  demonstration  of  the  rules — the  convenient  form  and  well- 
chosen  matter  of  the  tables,  as  well  as  in  the  complete  and  much  desired  appli- 
cation of  all  to  the  business  of  the  country,  the  “ University  Arithmetic”  of 
Prof.  Davies  is  superior  to  any  other  work  of  the  kind  with  which  we  are  ac- 
quainted. These,  with  the  many  other  improvements  introduced  by  the  ad- 
mirable scientific  arrangement  and  treatment  of  the  whole  subject,  and  in  par- 
ticular those  of  the  generalization  of  the  four  ground  rules,  so  as  to  include 
“ simple  and  denominate”  numbers  under  the  same  head,  and  the  very  plain 
demonstration  of  the  rule  for  the  division  of  fractions— both  of  which  are,  to  us, 
original — make  the  work  an  invaluable  one  to  teachers  and  students  who  are  de- 
sirous to  teach  or  study  arithmetic  as  a science  as  well  as  an  art. 

'.Signed.)  D H.  MAHAN,  Prof.  Engineering. 

W.  H.  O.  BARTLETT,  Prof.  Nat.  Phil. 

A.  E.  CHURCH,  Prof.  Mathematics. 

United  States  Military  Academy , Jan.  18,  1847. 


PRACTICAL  GEOMETRY  AND  MENSURATION. 

The  design  of  this  work  is  to  afford  schools  ana  academies  an  Elementary 
Text- Book  of  a practical  character.  The  introduction  into  our  schools,  within 
the  last  few  years,  of  the  subjects  of  Natural  Philosophy,  Astronomy,  Mineralo- 
gy, Chemistry,  and  Drawing,  has  given  rise  to  a higher  grade  of  elementary 
studies ; and  the  extended  application  of  the  mechanic  arts  calls  for  additional 
information  among  practical  men.  In  this  work  all  the  truths  of  Geometry  are 
made  accessible  to  the  general  reader,  by  omitting  the  demonstrations  altogether, 
and  relying  for  the  impression  of  each  particular  truth  on  a pointed  question  and 
an  illustration  by  a diagram.  In  this  way  it  is  believed  that  all  the  important 
properties  of  the  geometrical  figures  may  be  learned  in  a few  weeks  ; and  after 
these  properties  have  been  once  applied,  the  mind  receives  a conviction  of  their 
truth  little  short  of  what  is  afforded  by  rigorous  demonstration.  The  work  is 
divided  into  seven  books,  and  each  book  is  subdivided  into  sections. 

In  Hook  1 , the  properties  of  the  geometrical  figures  are  explained  bv  questions 
and  illustrations. 


Davies  System  uj  Mathematics. 


In  Book  II.  are  explained  the  construction  and  uses  of  the  various  scales ; and 
also  the  construction  of  geometrical  figures.  It  is,  as  its  title  imports,  Practica. 
Geometry. 

Book  III.  treats  of  Drawing.  Section  I„  of  the  Elements  of  the  Art ; Section 
II.,  of  Topographical  Drawing  ; and  Section  III.,  of  Plan  D rawing. 

Book  IV.  treats  of  Architecture — explaining  the  different  orders,  both  by  de- 
scriptions and  drawings. 

Book  V.  contains  the  application  of  the  principles  of  Geometry  to  the  Mensu- 
ration of  Surfaces  and  Solids.  A separate  rule  is  given  for  each  case,  and  the 
whole  is  illustrated  by  numerous  and  appropriate  examples. 

Book  VI.  contains  the  application  of  the  preceding  Books  to  Artificers’  and  Me- 
chanics’ work.  It  contains  full  explanations  of  all  the  scales — the  uses  to  which 
they  are  applied— and  specific  rules  for  the  calculations  and  computations  which 
are  necessary  in  practical  operations. 

Book  VII.  is  an  introduction  to  Mechanics.  It  explains  the  nature  and  proper- 
ties of  matter,  the  laws  of  motion  and  equilibrium,  and  the  principles  of  all  the 
simple  machines. 

ELEMENTARY  ALGEBRA. 

This  work  is  intended  to  form  a connecting  link  between  Arithmetic  and  Alge 
bra,  and  to  unite  and  blend,  as  far  as  possible,  the  reasoning  on  numbers  with  tho 
more  abstract  method  of  analysis.  It  is  intended  to  bring  the  subject  of  Algebra 
within  the  range  of  our  common  schools,  by  giving  to  it  a practical  and  tangible 
form.  It  begins  with  an  introduction,  in  which  the  subject  is  first  treated  men- 
tally, in  order  to  accustom  the  mind  of  the  pupil  to  the  first  processes ; after 
which,  the  system  of  instruction  assumes  a practical  form.  The  definitions  and 
rules  are  as  concise  and  simple  as  they  can  be  made,  and  the  reasonings  are  as 
clear  and  concise  as  the  nature  of  the  subject  will  admit.  The  strictest  scientific 
methods  are  always  adopted,  for  the  double  reason,  that  what  is  learned  should 
be  learned  in  the  right  way,  and  because  the  scientific  methods  are  generally  the 
most  simple. 

ELEMENTARY  GEOMETRY. 

This  work  is  designed  for  those  whose  education  extends  beyond  the  aequisi 
tion  of  facts  and  practical  knowledge,  but  who  have  not  the  time  to  go  through 
a full  course  of  mathematical  studies.  It  is  intended  to  present  the  striking  and 
important  truths  of  Geometry  in  a form  more  simple  and  concise  than  is  adopted 
in  Legendre,  and  yet  preserve  the  exactness  of  rigorous  reasoning.  In  this  sys- 
tem, nothing  has  been  omitted  in  the  chain  of  exact  reasoning,  nothing  has  been 
taken  for  granted,  and  nothing  passed  over  without  being  fully  demonstrated 
The  work  also  contains  the  applications  of  Geometry  to  the  Mensuration  of  Sur 
faces  and  Solids. 


SURVEYING. 

In  this  work  it  was  the  intention  of  the  author  to  begin  with  the  very  elements 
of  the  subject,  and  to  combine  those  elements  in  the  simplest  manner,  so  as  to 
render  the  higher  branches  of  Plane  Surveying  comparatively  easy.  All  the  in- 
struments needed  for  plotting  have  been  carefully  described,  and  the  uses  of  those 
required  for  the  measurement  of  angles  are  fully  explained.  The  Conventional 
Signs  adopted  by  the  Topographical  Bureau,  and  which  are  non  used  by  the  li nitea 
States  Engineers  in  all  their  charts  and  maps,  are  given  in  full.  An  account  is  also 
given  of  the  manner  of  surveying  the  public  lands  : and  although  the  method  is  sim 
pie,  it  has  nevertheless  been  productive  of  great  results.  The  work  also  contains 
a Table  of  Logarithms— a Table  of  Logarithmic  Sines— a Traverse  Table,  and  a 
Table  of  Natural  Sines— being  all  the  Tables  necessary  for  Practical  Surveying 

n\ 


Davies’  System  of  Mathematics. 


The  Collegiate  Course. 

I.  DAVIES’  BOURDON’S  ALGEBRA. 

II.  DAVIES’  LEGENDRE’S  GEOMETRY  AND  TRIGONOMETRY. 

III.  DAVIES’  ANALYTICAL  GEOMETRY. 

IV.  DAVIES’  DESCRIPTIVE  GEOMETRY. 

V.  DAVIES’  SHADES,  SHADOWS,  AND  PERSPECTIVE. 

VI.  DAVIES’  DIFFERENTIAL  AND  INTEGRAL  CALCULUS. 


The  works  embraced  under  the  head  of  the  “ Collegiate  Course,” 
were  originally  prepared  as  text-books  for  the  use  of  the  Military 
Academy  at  West  Point,  where,  with  a single  exception,  they  are 
still  used.  Since  their  introduction  into  many  of  the  colleges  of 
the  country,  they  have  been  somewhat  modified,  so  as  to  meet  the 
wants  of  collegiate  instruction.  The  general  plan  on  which  these 
works  are  written,  was  new  at  the  time  of  their  appearance.  Its 
main  feature  was  to  unite  the  logic  of  the  French  School  of 
Mathematics  with  the  practical  methods  of  the  English,  and  the 
two  methods  are  now  harmoniously  blended  in  most  of  our  systems 
of  scientific  instruction. 

The  introduction  of  these  works  into  the  colleges  was  for  a 
long  time  much  retarded,  in  consequence  of  the  great  deficiency  in 
the  courses  of  instruction  in  the  primary  schools  and  academies : 
and  this  circumstance  induced  Professor  Davies  to  prepare  his 
Elementary  Course. 

The  series  of  works  here  presented,  form  a full  and  complete 
course  of  mathematical  instruction,  beginning  with  the  first  com- 
binations of  arithmetic,  and  terminating  in  the  higher  applications 
of  the  Differential  Calculus.  Each  part  is  adapted  to  all  the 
others.  The  Definitions  and  Rules  in  the  Arithmetic,  have 
reference  to  those  in  the  Elementary  Algebra,  and  these  to  similar 
ones  in  the  higher  books.  A pupil,  therefore,  who  begins  this 
course  in  the  primary  school,  passes  into  the  academy,  and  then 
into  the  college,  under  the  very  same  system  of  scientific  in- 
struction. 

The  methods  of  teaching  are  all  the  same,  varied  only  by  the 
lature  and  difficulty  of  the  subject.  He  advances  steadily  from 
one  grade  of  knowledge  to  another,  seeing  as  he  advances  the  con 
nection  and  mutual  relation  of  all  the  parts  : and  when  he  reacnej 
the  end  of  his  course,  he  finds  indeed,  that  “ science  is  but  know 
ledge  reduced  to  order.” 

(81 


Davies'  System  of  Mathematics. 


DAVIES’  BOURDON. 

The  Treatise  on  Algebra  by  M.  Bourdon,  is  a work  of  singular  excellence 
and  merit.  In  France  it  is  one  of  the  leading  text-books.  Shortly  after  its  first 
publication  it  passed  through  several  editions,  and  has  formed  the  basis  of  every 
subsequent  work  on  the  subject  of  Algebra. 

The  original  work  is,  however,  a full  and  complete  treatise  on  the  subject  of 
Algebra,  the  later  editions  containing  about  eight  hundred  pages  octavo.  The 
time  given  to  the  study  of  Algebra  in  this  country,  even  in  those  seminaries  where 
the  course  of  mathematics  is  the  fullest,  is  too  short  to  accomplish  so  volumin- 
ous a work,  and  hence  it  has  been  found  necessary  either  to  modify  it,  or  to 
abandon  it  altogether.  The  Algebra  of  M.  Bourdon,  however,  has  been  regarded 
only  as  a standard  or  model,  and  it  would  perhaps  not  be  just  to  regard  him  as 
responsible  for  the  work  in  its  present  form. 

In  this  work  are  united  the  scientific  discussions  of  the  French  with  the  prac- 
tical methods  of  the  English  school,  so  that  theory  and  practice,  science  and  art, 
may  mutually  aid  and  illustrate  each  other.  A great  variety  of  examples  have 
also  been  added  in  the  late  editions. 

DAVIES’  LEGENDRE. 

Legendre’s  Geometry  has  taken  the  place  of  Euclid,  to  a great  extent,  both  in 
Europe  and  in  this  country.  In  the  original  work  the  propositions  are  not 
enunciated  in  general  terms,  but  with  reference  to,  and  by  the  aid  of,  the  par- 
ticular diagrams  used  for  the  demonstrations.  It  was  supposed  that  this  de 
parture  from  the  method  of  Euclid  had  been  generally  regretted,  and  among  the 
many  alterations  made  in  the  original  work,  to  adapt  it  to  the  systems  of  i e- 
struction  in  this  country,  that  of  enunciating  the  propositions  in  general  terms 
should  be  particularly  named  ; and  this  change  has  met  with  universal  acceptance. 

To  the  Geometry  is  appended  a system  of  Mensuration  of  Planes  and  Solids— 
a full  treatise  on  Plane  and  Spherical  Trigonometry— and  a table  of  Logarithms, 
and  Logarithmic  Sines,  Tangents,  and  Secants.  The  whole  forms  a complete 
system  of  Geometry  with  its  applications  to  Trigonometry  and  Mensuration, 
together  with  the  necessary  tables. 

ANALYTICAL  GEOMETRY. 

This  work  embraces  the  investigation  of  the  properties  of  geometrical  figures 
oy  means  of  analysis.  It  commences  with  the  elementary  principles  of  the  sci- 
ence, discusses  the  Equation  of  the  Straight  Line  and  Circle — the  Properties  of 
the  Conic  Sections — the  Equation  of  the  Plane — the  Positions  of  Lines  in  Space, 
and  the  Properties  of  Surfaces. 

DESCRIPTIVE  GEOMETRY. 

Descriptive  Geometry  is  intimately  connected  with  Architecture  and  Civil 
Engineering,  and  affords  great  facilities  in  all  the  operations  of  Construction. 

As  a mental  discipline,  the  study  of  it  holds  the  first  place  among  the  various 
branches  of  Mathematics. 

SHADES,  SHADOWS,  AND  PERSPECTIVE. 

This  work  embraces  the  various  applications  of  Descriptive  Geometry  to 
Drawing  and  Linear  Perspective. 

DIFFERENTIAL  AND  INTEGRAL  CALCULUS. 

This  treatise  on  the  Differential  and  Integral  Calculus,  was  intended  to  supp.y 
the  higher  seminaries  of  learning  with  a text-book  on  that  branch  of  science.  It 
is  a work  after  the  French  methods  of  teaching,  and  in  which  the  notation  of  tin 
French  school  is  adopted. 

fP 


Davies’  Mathematical  Works. 


A CATALOGUE 

OF  THE 

COLLEGES  AND  UNIVERSITIES 

THAT  HAVE  ADOPTED 

DAVIES’  MATHEMATICAL  WORKS. 

(THE  WHOLE  SERIES,  OR  IN  PART.) 


THE  UNITE!)  STATES  MILITARY  ACADEMY. 


Dartmouth  College, 

University  of  Vermont, 
Norwich  University, 

Brown  University, 

Washington  College, 

Wesleyan  University, 

Columbia  College, 

Union  College, 

Hamilton  Lit.  and  Theol.  Instil. 
Geneva  College, 

University  of  New  York, 
College  of  New  Jersey, 
University  of  Pennsylvania, 
Lafayette  College, 

Marsh  ill  College, 

Dickinson  College, 

Jefferson  College, 

Washington  College, 

Alleghany  College, 

Western  University, 

Newark  College, 

Georgetown  College, 
Columbian  College, 

St.  John’s  College, 

St.  Mary’s  College, 

Mount  St.  Mary’s  College, 
Washington  College, 


Hanover, 

New  Hampshire 

Burlington , 

Vermont. 

Norwich, 

Providence, 

Rhode  Island. 

Hartford, 

Connecticut. 

Middletown, 

“ 

New  York, 

New  York. 

Schenectady, 

14  ,4 

Hamilton, 

“ “ 

Geneva, 

.4 

New  York, 

4.  .4 

Princeton. 

New  Jersey. 

Philadelphia, 

Pennsylvania. 

Easton, 

4* 

Mercersburg, 

U 

Carlisle, 

44 

Canonsburg. 

44 

Washington, 

44 

Meadville, 

44 

Pittsburg, 

44 

Newark, 

Delaware. 

Georgetown . 

Dist.  of  Columrl 

Washington, 

It  4* 

Annapolis, 

Maryland, 

Baltimore, 

“ 

Emmettsburg, 

“ 

Lexingtgn, 

Virginia. 

10 

Davies’  Mathematical  Works. 


Hamp>den-Sydney  College, 
University  of  Virginia, 
Randolph  Macon  College, 
University  of  North  Carolina, 
Davidson  College, 

College  of  South  Carolina, 
University  of  Alabama, 
Lagrange  College, 

Louisiana  College, 

Jefferson  College, 

Oakland  College, 

University  of  Tennessee, 

St.  Joseph’s  College, 

Centre  College, 

Augusta  College, 

Cumberland  College, 
Georgetown  College, 

Bacon  College, 

University  of  Ohio, 

Western  Reserve  College, 
Oberlin  Institute, 

Miami  University, 

Franklin  College, 

Kenyon  College, 

Granville  College, 

Cincinnati  College, 
Woodward  College, 

Indiana  College, 

South  Hanover  College, 
Wabash  College, 

Illinois  College, 

Shurtleff  College, 
McKendroan  College, 
University  of  St.  Louis, 

St.  Charles  College, 

Michigan  University, 

Tbe  Miiitary  Academy, 
Charleston  College, 


Prince  Ed  Co. 

Virginia. 

Charlottesville, 

“ 

Boydtown, 

U 

Chapel-Hill, 

North  Carolina 

Mecklenburg, 

tl 

Columbia, 

South  Carolina 

Tuscaloosa, 

Alabama. 

Lagrange, 

“ 

Jackson, 

Louisiana. 

Washington, 

Mississippl 

Oakland, 

W 

Nashville, 

Tennessee. 

Bardstown, 

Kentucky. 

Danville, 

(* 

Augusta, 

“ 

Princeton, 

1C 

Georgetown, 

“ 

Harrodsburgh, 

“ 

Athens, 

Ohio. 

Hudson, 

U 

Oberlin, 

it 

Oxford, 

“ 

New  Athens, 

- 

Gambier, 

a 

Granville, 

- 

Cincinnati, 

- 

Cincinnati, 

“ 

Bloomington, 

Indiana 

South  Hanover, 

“ 

Crawford  sviUe, 

“ 

Jacksonville, 

Illinois 

Upper  Alton, 

“ 

Lebanon, 

it 

St.  Louis, 

Missouri 

St.  Charles, 

■ U 

Ann  Arbour, 

Michigan 

Georgetown, 

Kentucky. 

Charleston , i 

South  Carolina 

11 


Parker' a Natural  riulosophy. 


NATURAL  AND  EXPERIMENTAL  PHILOSOPHY 

FOR  SCHOOLS  AND  ACADEMIES, 

BY  R.  G.  PARKER,  A.  M. 

PRINCIPAL  OF  THE  JOHNSON  GRAMMAR  SCHOOL,  BOSTON,  AUTHOR  OF  AIDS 
TO  ENGLISH  COMPOSITION,  ETC.,  ETC. 


I.  PARKER’S  FIRST  LESSONS  IN  NATURAL  PHILOSOPHY. 

II.  PARKER’S  COMPENDIUM  OF  NATURAL  AND  EXPERIMENTAL 
PHILOSOPHY. 


PARKER’S  FIRST  LESSONS  IN  NATURAL  PHILOSOPHY, 
Embracing  the  Elements  of  the  Science.  Illustrated  with  numerous 
engravings.  Designed  for  young  beginners.  Price  38  cts. 

It  is  the  design  of  this  Utile  book,  to  present  to  the  minds  of  the 
youth  of  the  country  a view  of  the  laws  of  Nature— as  they  are 
exhibited  in  the  Natural  World. 

Reading  books  should  be  used  in  schools  for  the  double  object  of 
teaching  the  child  to  read,  and  storing  his  mind  with  pleasant  and 
useful  ideas. 

The  form  of  instruction  by  dialogue,  being  the  simplest,  has 
been  adopted — and  by  means  of  the  simple  question  and  the  ap- 
propriate answer,  a general  view  of  the  laws  of  the  physical  uni- 
verse has  been  rendered  so  intelligible,  as  to  be  easily  understood 
by  children  who  are  able  to  read  intelligibly. 

It  is  confidently  believed  that  this  book  will  form  an  importanl 
eia  in  the  progress  of  common-school  education 

PARKER’S  COMPENDIUM  OF  NATURAL  AND  EXPERIMENTAL 
PHILOSOPHY. 

Embracing  the  Elementary  principles  of  Mechanics,  Hydrostatics,  Hy- 
draulics, Pneumatics,  Acoustics,  Pyronomics,  Optics,  Astronomy, 
Galvanism,  Magnetism,  Electro-Magnetism,  Magneto-Electricity, 
with  a description  of  the  Steam  and  Locomotive  Engines.  Illustrated 
by  numerous  diagrams.  Price  $1.00. 

The  use  of  school  apparatus  for  illustrating  and  exemplifying 
the  principles  of  Natural  and  Experimental  Philosophy,  has,  with- 
in the  last  few  years,  become  so  general  as  to  render  necessary  a 
work  which  should  combine,  in  the  same  course  of  instruction,  the 
theory,  with  a full  description  of  the  apparatus  necessary  for  illus- 
tration and  experiment. 

The  work  of  Professor  Parker,  it  is  confidently  believed,  fully 
oiwets  that  requirement.  It  is  also  verv  full  in  the  general  facts 

(U) 


Parker's  Natural  Philosophy. 


which  it  presents — clear  and  concise  in  its  style,  and  entirely 
scientific  and  natural  in  its  arrangement.  The  following  features 
will,  it  is  hoped,  commend  the  work  to  public  favor. 

1.  It  is  adapted  to  the  present  state  of  natural  science  ; embraces 
a wider  field,  and  contains  a greater  amount  of  information  on  the 
respective  subjects  of  which  it  treats,  than  any  other  elementary 
treatise  of  its  size. 

2.  It  contains  an  engraving  of  the  Boston  School  set  of  philn 
sophical  apparatus  ; a description  of  the  instruments,  and  an  ac- 
count of  many  experiments  which  can  he  performed  by  means  ot 
the  apparatus. 

3 It  is  enriched  by  a representation  and  a description  of  the 
Locomotive  and  the  Stationary  Steam  Engines , in  their  latest  and 
most  approved  form3. 

4.  Besides  embracing  a copious  account  of  the  principles  ol 
Electricity  and  Magnetism,  its  value  is  enhanced  by  the  introduc- 
tion of  the  science  of  Pyronomics,  together  with  the  new  science 
of  Electro-Magnetism  and  Magneto-Electricity. 

5.  It  is  peculiarly  adapted  to  the  convenience  of  study  and  of 
recitation,  by  the  figures  and  diagrams  being  first  placed  side  by 
side  with  the  illustrations,  and  then  repeated  on  separate  leaves  at 
the  end  of  the  volume.  The  number  is  also  given,  where  each 
principle  may  be  found,  to  which  allusion  is  made  throughout  the 
volume. 

6.  It  presents  the  most  important  principles  of  science  in  a 
larger  type  ; while  the  deductions  from  these  principles,  and  the 
illustrations,  are  contained  in  a smaller  letter.  Much  useful  and 
interesting  matter  is  also  crowded  into  notes  at  the  bottom  of  the 
page.  By  this  arrangement,  the  pupil  can  never  be  at  a loss  to 
distinguish  the  parts  of  a lesson  which  are  of  primary  importance  ; 
nor  will  he  be  in  danger  of  mistaking  theory  ami  conjecture  for  fact. 

7.  It  contains  a number  of  original  illustrations,  which  the  author 
has  found  more  intelligible  to  young  students  than  those  which  he 
has  met  elsewhere. 

8.  Nothing  has  been  omitted  which  is  usually  contained  in  an 
elementary  treatise. 

9.  A full  description  is  given  of  the  Magnetic  Telegraph,  and  the 
principles  of  its  construction  are  fully  explained. 

10.  For  the  purpose  of  aiding  the  teacher  in  conducting  an  ex- 
amination through  an  entire  subject,  or  indeed,  through  the  whole 
book,  if  necessary,  all  the  diagrams  have  been  repeated  at  the 
end  of  the  work,  and  questions  proposed  on  the  left-hand  page  im- 
mediately opposite.  This  arrangement  will  permit  ihe  pupil  to 
use  the  figure,  in  his  recitation,  if  he  have  not  time  to  make  it  on 
the  black-boa.  d.  and  will  also  enable  him  to  review  several  lessons 
and  rec  all  all  the  principles  by  simply  reading  the  questions,  and 
analyzing  the  diagrams. 


Parker's  Natural  Philosophy. 


From  the  Wayne  County  Whig. 

After  a careful  examination  of  this  work,  we  find  that  it  is  well  calculated  for 
the  purpose  for  which  it  is  intended,  and  better  adapted  to  the  state  of  natural 
science  at  the  present  time,  than  any  other  similar  production  with  which  we 
are  acquainted.  The  design  of  the  author,  in  the  preparation  of  this  work,  was 
to  present  to  the  public  an  elementary  treatise  unencumbered  with  matter  that  is 
not  intimately  connected  with  this  science,  and  to  give  a greater  amount  of  in- 
formation on  the  respective  subjects  of  which  it  treats,  than  any  other  school- 
book of  an  elementary  character.  The  most  remarkable  feature  in  the  style  of 
this  work  is  its  extreme  brevity  In  the  arrangement  of  the  subject  and  the  man 
ner  of  presenting  it,  there  are  some  peculiarities  which  are,  in  our  opinion,  de- 
cided improvements.  The  more  important  principles  of  this  interesting  science 
are  given  in  a few  words,  and  with  admirable  perspicuity,  in  a larger  type  ; while 
the  deductions  from  these  principles,  and  the  illustrations  are  contained  in  a 
smaller  letter.  Much  useful  and  interesting  matter  is  also  given  in  notes  at  the 
oottoin  of  the  page. 

This  volume  is  designed  expressly  to  accompany  the  Boston  School  Srt  of  Philo- 
sophical  .Apparatus ; but  the  numerous  diagrams  with  which  it  is  illustrated,  are 
so  well  executed  and  so  easily  understood,  that  the  assistance  of  the  Apparatus 
is  hardly  necessary  to  a thorough  knowledge  of  the  science.  The  trustees  of  the 
Lyons  Union  School  having  recently  procured  a complete  set  of  the  above  Ap- 
paratus, this  work  will  now  be  used  as  a text-book  in  that  institution. 


Leicester  Academy,  April  12,  1848. 

Messrs.  A.  S.  Barnes  & Co.: 

Sirs: — I have  examined  Parker’s  Natural  Philosophy,  and  anj  much  pleased 
with  it.  1 think  I shall  introduce  it  into  the  academy  the  coining  term.  It  seems 
to  me  to  have  hit  a happy  medium  betw  een  the  too  simple  and  the  too’abstract. 
The  notes  containing  facts,  and  showing  the  reasons  of  many  things  that  are  of 
common  occurrence  m every-day  life,  seem  to  me  to  be  a valuable  feature  of  the 
work. 

Very  respectfully,  yours,  B.  A.  SMITH. 


From  the  New  York  Evening  Post. 

Professor  Parker’s  book  embraces  the  latest  results  of  investigation  on  the  sul 
'ects  of  which  it  treats.  It  has  a separate  title  for  the  laws  of  heat,  or  Pyronom 
lcs,  which  have  been  lately  added  to  the  list  of  sciences,  as  well  as  electro  mag- 
netism and  magneto  electricity.  The  matter  is  well  arranged,  and  the  style  of 
statement  clear  and  concise.  The  figures  and  diagrams  are  placed  side  by  side 
with  the  text  they  illustrate,  which  is  greatly  for  the  convenience  of  the  student- 
We  cheerfully  commend  the  book  to  the  favorable  attention  of  the  public. 


From  the  Jllbany  Spectator. 

'I  his  is  a school-book  of  no  mean  pretensions  and  of  no  ordinary  value.  It  is 
admirably  adapted  to  the  present  state  of  natural  science  ; and  besides  contain- 
ing engravings  of  the  Boston  school  set  of  philosophical  apparatus,  embodies 
>ii  ire  information  on  every  subject  on  which  it  treats  than  any  other  elementary 
'*■  rk  of  its  size  that  we  have  examined  It  abounds  with  all  the  necessary  heips 
m 'rosecuting  the  study  of  the  science,  and  as  its  value  becomes  known  it  can- 
faii  to  be  generally  adopted  as  a text-book 


14 


Parker  $ Natural  Philosophy. 


From  the  Newark  Daily  Advertiser. 

A work  adapted  to  the  present  state  of  natural  science  is  greatly  needed  in  all 
our  schools,  and  the  appearance. of  one  meeting  all  ordinary  wants  must  be  hailed 
with  pleasure  by  those  who  feel  an  interest  in  the  cause  of  education.  Mr.  Par- 
ker’s work  embraces  a wider  field,  and  contains  a greater  amount  of  information 
on  the  respective  subjects  of  which  it  treats,  than  any  other  elementary  treatise 
of  its  size,  and  is  rendered  peculiarly  valuable  by  the  introduction  of  the  science  of 
Pyronomics,  together  with  the  new  sciences  of  Electro-Magnetism  and  Magneto 
Electricity.  We  have  seldom  met  wdth  a work  so  well  adapted  to  the  conveni- 
ence of  study  and  recitation,  and  regard  as  highly  worthy  of  commendation  the 
care  which  the  author  has  taken  to  prevent  the  pupil  from  mistaking  theory  and 
conjecture  for  fact.  We  predict  for  this  valuable  and  beautifully  printed  w 
the  utmost  success. 

From  the  New  York  Courier  and  Enquirer 

“ A School  Compendium  of  Natural  and  Experimental  Philosophy,”  by  Richard 
Green  Parker,  has  just  been  issued  by  Barnes  &.  Co.  Mr.  Parker  has  had  a good 
deal  of  experience  in  the  business  of  practical  instruction,  and  is,  also,  the  author 
of  works  which  have  been  widely  adopted  in  schools.  The  present  volume  strikes 
us  as  having  very  marked  merit,  and  we  cannot  doubt  it  will  be  well  received. 


New  York,  May . 1848. 

Messrs.  A.  S.  Barnes  & Co.-. 

Gent. I have  no  hesitation  in  saying  that  Parker’s  Natural  Philosophy  is  the 
most  valuable  elementary  work  I have  seen  : the  arrangement  of  the  subjects 
and  the  clearness  of  the  definitions  render  it  an  excellent  adjunct  to  a teacher. 
For  the  last  seven  years  I have  used  it  in  various  schools  as  a text-book  for  my 
lectures  on  Natural  Philosophy,  and  am  happy  to  find  that  in  the  new  edition 
much  important  matter  is  added,  more  especially  on  the  subjects  of  Electricity 
and  Electro-Magnetism. 

With  respect,  Gentlemen, 

Your  obedient  servant, 

GILBERT  LANGDON  HUME, 
Teacher  of  Natural  Philosophy  and  Mathematics  in  N.  Y.  city. 


New  York,  May  2,  1848 

We  have  used  Parker’s  Compend  of  Natural  Philosophy  for  many  years,  and 
consider  it  an  excellent  work  on  the  various  topics  of  which  it  treats. 

Yours,  &c.  FORREST  &.  McELLIGOTT, 

Principals  of  the  Collegiate  School 


From  the  Lynchburg  Virginian. 

The  volume  before  us  strikes  us  as  containing  more  to  recommend  it  than  any 
one  of  its  class  with  which  we  are  acquainted.  It  is  adapted  to  the  present  state 
of  natural  science ; embraces  a wider  field,  and  contains  a greater  amount  of  in- 
formation on  the  respective  subjects  of  which  it  treats,  than  any  other  clement. iry 
treatise  of  its  size.  It  contains  descriptions  of  the  steam-engine,  stationery  and 
locomotive,  and  of  the  magnetic  telegraph.  It  embraces  a copious  account  o' 
the  principles  of  electricity  and  magnetism,  under  all  their  modifications,  and  is 
embellished  by  a vast  number  of  illustrations  and  diagrams.  There  is  appended 
a series  of  questions  for  examination,  copious  and  pertinent 


15 


Gillespie's  Manna1  of  Road- Making. 


ROADS  AND  RAILROADS. 


A MANUAL  OF  ROAD-MAKING: 


Comprising  the  principles  and  practice  of  the  Location,  Construe  • 
tion,  and  Improvement  of  Roads,  (common,  macadam,  paved 
plank,  &c.,)  and  Railroads.  By  W.  M.  Gillespie,  A.  M., 
Professor  of  Civil  Engineering  in  Union  College.  Price  $1.50. 


Recommendation  from  Professor  Mahan . 

I have  very  carefully  looked  over  Professor  Gillespie’s  Manual  of  Road- 
Making.  It  is,  in  all  respects,  the  best  work  on  this  subject  with  which  I am  ac- 
quainted ; being,  from  its  arrangement,  comprehensiveness  and  clearness,  equally 
adapted  to  the  wants  of  Students  of  Civil  Engineering,  and  the  purposes  of  per 
sons  in  any  way  engaged  in  the  construction  or  supervision  of  roads.  The  ap- 
pearance of  such  a work,  twenty  years  earlier,  would  have  been  a truly  national 
benefit,  and  it  is  to  be  hoped  that  its  introduction  into  our  seminaries  may  be  so 
general  as  to  make  a knowledge  of  the  principles  and  practice  of  this  branch  of 
engineering,  as  popular  as  is  its  importance  to  all  classes  of  the  community. 

(Signed,) 

D.  H.  MAHAN, 

Professor  of  Civil  Engineering  in  the  Military  ) 
Academy  of  the  United  States.  j 


From  a Report  of  a Committee  of  the  American  Institute. 

This  work  contains  in  a condensed  form,  all  the  principles,  both  ancient  and 
modern,  of  this  most  important  art ; and  almost  every  thing  useful  in  the  great 

mass  of  writers  on  this  subject Such  a work  as  this  performs  a great 

service  for  those  who  are  destined  to  construct  roads — by  showing  not  only  what 
ought  to  be  done,  but  what  ought  not  to  be  done  ; thus  saving  immense  outlay  of 
money,  and  loss  of  time  in  experiments The  committee  therefore,  recom- 

mend it  to  the  public. 

From  the  American  Railroad  Journal. 

The  views  of  the  author  are  sound  and  practical,  and  should  be  read  by  the 
people  throughout  the  entire  length  and  breadth  of  the  land.  . . . We  recom- 
mend this  Manual  to  the  perusal  of  every  tax-payer  for  road-making,  and  to  the 
young  men  of  the  country,  as  they  will  find  useful  information  in  relation  to  each 
department  of  road-making,  which  will  surely  be  useful  to  them  in  after-life. 


From  Silli man's  American  Journal  of  Science. 

If  the  well-established  principles  of  Road-Making,  which  are  so  plainly  set 
forth  in  Prof.  Gillespie’s  valuable  work,  and  so  well  illustrated,  could  be  once 
pat  into  general  use  in  this  country,  every  traveller  would  bear  testimony  to  the 
fact  that  the  author  is  a great  public  benefactor. 

From  the  Journal  of  the  Franklin  Institute. 

This  small  volume  contains  much  valuable  matter,  derived  from  the  best 
authorities,  and  set  forth  in  a clear  and  simple  style.  For  the  want  of  informa- 
tion which  is  contained  in  this  Manual,  serious  mistakes  are  frequently  made, 
and  roads  are  badly  located  and  badly  constructed  by  persons  ignorant  of  the 

(Id) 


Gillespie's  Manual  of  Road- Making. 


principles  which  ought  to  govern  in  such  cases.  By  the  extensive  circulati  of 
such  books  as  that  now  before  us,  and  the  imparting  of  sound  views  on  tin  it- 
ject  to  the  students  of  our  collegiate  institutions,  we  may  hope  for  a chani  for 
.he  better  in  this  respect. 

From  the  Albany  Cultivator. 

The  author  of  this  work  has  supplied  a desideratum  which  has  long  existed 
Perhaps  there  is  no  subject  on  which  information  is  more  needed  by  the  country 
in  general  than  that  of  Road-Making.  Prof.  Gillespie  has  taken  up  the  subject 
in  a proper  manner,  beginning  the  work  at  the  right  place,  and  prosecuting  it  in 
systematic  order  to' its  completion. 

From  the  New  York  Tribune. 

It  would  astonish  many  “ path-masters”  to  see  how  much  they  don’t  know 
with  regard  to  the  very  business  they  have  considered  themselves  such  adepts  in. 
Yet  all  is  so  simple,  so  lucid,  so  straightforward,  so  manifestly  true,  that  the 
most  ordinary  and  least  instructed  mind  cannot  fail  to  profit  by  it.  We  trust  this 
useful  and  excellent  volume  may  find  its  way  into  every  village  library  if  not 
into  every  school  library,  as  well  as  into  the  hands  of  every  man  interested  in 
road-making.  Its  illustrations  are  very  plain  and  valuable,  and  we  cannot  doubt 
that  the  work  will  be  a’  welcome  visiter  in  many  a neighborhood,  and  that  bad 
roads  will  vanish  before  it. 

From  the  Newark  Daily  Advertiser. 

This  elaborate  and  admirable  work  combines  in  a systematic  and  symmetrical 
form  the  results  of  an  engineering  experience  in  all  parts  of  the  Union,  and  of  an 
examination  of  the  great  roads  of  Europe,  with  a careful  digestion  of  all  acces- 
sible authorities.  The  six  chapters  into  which  it  is  divided  comprehend  a 
methodical  treatise  upon  every  part  of  the  whole  subject ; showing  what  roads 
ought  to  be  in  the  vital  points  of  direction,  slopes,  shape,  surface,  and  cost,  and 
giving  methods  of  performing  all  the  necessary  measurements  of  distances,  di 
rections,  and  heights,  without  the  use  of  any  instruments  but  such  as  any 
mechanic  can  make,  and  any  farmer  use.  Bridges,  Railroads,  and  City  Streets 
are  also  treated  of  at  length  and  with  good  sense. 


From  the  Vermont  Chronicle. 

To  selectmen  and  others  who  may  have  any  thing  to  do  with  these  improve- 
ments, we  would  earnestly  recommend  the  book  named  above.  The  author  is  a 
man  of  science,  (Professor  of  Civil  Engineering  at  Union  College,)  and  his  work 
embraces  a full  discussion  of  both  the  principles  and  practice  of  Road-Making 
A little  study  of  this  work  may  often  lead  to  results  of  importance  to  whole  towns 
and  counties. 


From  the  Home  Journal. 

The  author  of  this  book  holds  a quill  so  skilful  and  dair tv  in  light  literature, 
that  we  were  not  prepared  with  laurels  to  crown  him  for  a scientific  work  but 
we  see,  by  the  learned  critics,  that  this  fruit  of  his  study  of  his  profession  as  an 
engineer,  is  very  worthy  of  high  commendation,  and  a valuable  addition  to  the 
useful  literature  of  the  day. 


Willard’s  Series  of  School  Histories  and  Charts. 


MRS.  EMMA  WILLARD’S 

SERIES  OF  SCHOOL  HISTORIES  AND  CHARTS. 

I.  WILLARD’S  HISTORY  OF  THE  UNITED  STATES,  OR  RE- 
PUBLIC OF  AMERICA.  8vo.  Price  $1.50. 

II.  WILLARD’S  SCHOOL  HISTORY  OF  THE  UNITED  STATES. 

III.  WILLARD'S  AMERICAN  CHRONOGRAPHER,  $1.00. 

A Chart  op  American  History. 


I.  WILLARD’S  UNIVERSAL  HISTORY  IN  PERSPECTIVE.  $1.50. 
II.  WILLARD’S  TEMPLE  OF  TIME,  $1.25. 

A Chart  of  Universal  History 


WILLARD’S 

HISTORY  OF  THE  UNITED  STATES. 


The  large  work  is  designed  as  a Text-Book  for  Academies  and 
Female  Seminaries:  and  also  for  District  School  and  Family 
Libraries.  The  small  work  being  an  Abridgment  of  the  same,  is 
designed  as  a Text-Book  for  Common  Schools.  The  originality 
of  the  plan  consists  in  dividing  the  time  into  periods , of  which 
the  beginnings  and  terminations  are  marked  by  important  events ; 
and  constructing  a series  of  maps  illustrating  the  progress  of  the 
settlement  of  the  country , and  the  regular  advances  of  civilization. 
The  Chronographic  Chart,  gives  by  simple  inspection,  a view  of 
the  divisions  of  the  work,  and  the  events  which  mark  the  be- 
ginning and  termination  of  each  period  into  which  it  is  divided. 
A full  chronological  table  will  be  found,  in  which  all  the  events  of 
the  History  are  arranged  in  the  order  of  time.  There  is  appended 
to  the  work  the  Constitution  of  the  United  States,  and  a series  ol 
questions  adapted  to  each  chapter,  so  that  the  work  may  be  used 
in  schools  and  for  private  instruction. 

The  Hon.  Daniel  Webster  says,  of  an  early  edition  of  the  above  work,  in  a letter 
to  the  author,  4*  7 keep  it  near  me,  as  a Booh  of  Reference , accurate  in  facts  and  dates.1* 

0 8 


Willard’s  Series  of  School  Histories  and  Charts. 


WILLARD’S 

AMERICAN  C H RONOGRAPH  ER, 

DESIGNED  TO  ACCOMPANY  WILLARD’S  HISTORY  OP 
THE  UNITED  STATER 


To  measure  time  by  space  is  universal  .among  civilized  nations, 
and  as  the  hours,  and  minutes,  and  seconds  of  a clock  measure  the 
time  of  a day,  so  do  the  centuries,  tens,  and  single  years  of  this 
Chronographer,  measure  the  time  of  American  History.  A 
general  knowledge  of  chronology  is  as  indispensable  to  history,  as 
a general  knowledge  of  latitude  and  longitude  is  to  geography. 
But  to  learn  single  dates,  apart  from  a general  plan  of  chronology 
addressed  to  the  eye,  is  as  useless  as  to  learn  latitudes  and  longi- 
tudes without  reference  to  a map.  The  eye  is  the  only  medium 
of  permanent  impression.  The  essential  point  in  a date,  is  to 
know  the  relative  place  of  an  event,  or  how  it  stands  in  time  com- 
pared with  other  important  events.  The  scholar  in  the  school- 
100m,  or  the  gentleman  in  his  study,  wants  such  a visible  plan  of 
time  for  the  study  of  history,  the  same  as  he  wants  the  visible 
plan  of  space,  viz.,  a map  for  the  study  of  geography,  or  of  books 
of  travels.  Such  is  the  object  of  Willard's  Chronographer  of 
American  History. 

Extract  from  a Report  of  the  Ward  School  Teachers ’ Association 
of  the  City  of  New  York. 

The  Committee  on  Books  of  the  Ward  School  Association  respectfully  report . 

That  they  have  examined  Mrs.  Willard’s  History  of  the  United  States  with 
peculiar  interest,  and  are  free  to  say,  that  it  is  in  their  opinion  decidedly  the  best 
treatise  on  this  interesting  subject  that  they  have  seen.  * * 

As  a school-book,  its  proper  place  is  among  the  first.  The  language  is  remark- 
able for  simplicity,  perspicuity,  and  neatness ; youth  could  not  be  trained  to  a 
better  taste  for  language  than  this  is  calculated  to  impart.  The  history  is  so 
written  as  to  lead  to  geographical  examinations,  and  impresses  by  practice  the 
habit  to  read  history  with  maps.  It  places  at  once,  in  the  hands  of  American 
youth,  the  history  of  their  country  from  the  day  of  its  discovery  to  tne  present 
time,  and  exhibits  a clear  arrangement  of  all  the  great  and  good  deeds  of  the'r 
ancestors,  of  which  they  now  enjoy  the  benefits,  and  inherit  the  renown.  The 
struggles,  sufferings,  firmness,  and  piety  of  the  first  settlers  are  delineated  with  a 
masterly  hand. 

The  gradual  enlargement  of  our  dominions,  and  the  development  of  our  na- 
tional energies,  are  traced  with  a minute  accuracy,  which  the  general  plan  of  the 
work,  indicates. 

The  events  and  achievements  of  the  Revolution  and  of  the  last  war,  are 
brought  out  in  a clear  light,  and  the  subsequent  history  of  our  national  policy 
and  advancement  striking! v portrayed,  without  being  disfigured  bv  that  tinge 

(IT 


Willard's  Series  oj  School  Histories  and  Charts. 


ol  party  bias  which  is  so  difficult  to  be  guarded  against  by  historians  of  their  own 
times. 

The  aetails  of  the  discovery  of  this  continent  by  Columbus,  and  of  the  early 
settlements  by  the  Spaniards,  Portuguese,  and  other  European  nations,  are  all  of 
essential  interest  to  the  student  of  American  history,  and  will  be  found  sufficiently 
minute  to  render  the  history  of  the  continent  full  and  complete.  The  different 
periods  of  time,  together  with  the  particular  dates,  are  distinctly  set  forth  with 
statistical  notes  on  the  margin  of  each  page, — and  these  afford  much  inf  rmation 
without  perusing  the  pages. 

The  maps  are  beautifully  executed,  with  the  locality  of  places  where  particular 
events  occurred,  and  the  surrounding  country  particularly  delineated.  These 
are  admirably  calculated  to  make  lasting  impressions  on  the  mind. 

The  day  has  now  arrived  when  every  child  should  be  acquainted  with  the  his- 
tory of  his  country  ; and  your  Committee  rejoice  that  a work  so  full  and  clear  can 
be  placed  within  the  reach  of  every  one. 

The  student  will  leam,  by  reading  a few  pages,  how  much  reason  he  has  to  be 
proud  of  his  country— of  its  institutions — of  its  founders — of  its  heroes  and  states- 
men : and  by  such  lessons  are  we  not  to  hope  that  those  who  come  after  us  wTn 
be  instructed  in  their  duties  as  citizens,  and  their  obligations  as  patriots  1 

Your  Committee  are  anxious  to  see  this  work  extensively  used  in  all  the  schools 
in  the  United  States. 


(Signed,) 

SENECA  DURAND, 
EDWARD  McELROY, 
JOHN  WALSH. 


The  Committee  would  respectfully  offer  the  following  resolution  : 

Resolved,  That  Mrs.  Emma  Willard’s  History  of  the  United  States  be  adopted 
by  this  Association,  and  its  introduction  into  our  schools  earnestly  recom- 
mended. 

At  a meeting  of  the  Board  of  the  Ward  School  Teacners’  Association,  January 
20th,  1847,  the  above  Resolution  was  adopted. — (Copied  from  the  Minutes.) 


From  the  Boston  Traveller. 

We  consider  the  work  a remarkable  one,  in  that  it  forms  the  best  book  for 
general  reading  and  reference  published,  and  at  the  same  time  has  no  equal,  in 
our  opinion,  as  a text-book.  On  this  latter  point,  the  profession  which  its  author 
has  so  long  followed  with  such  signal  success,  rendered  her  peculiarly  a fitting 
person  to  prepare  a text-book.  None  but  a practical  teachei  is  capable  of  pre- 
paring a good  school-book ; and  as  woman  has  so  much  to  do  in  forming  our 
early  character,  why  should  her  influence  cease  at  the  fireside — why  not  en- 
courage her  to  exert  her  talents  still,  in  preparing  school  and  other  books  for 
after  years  1 No  hand  can  do  it  better. 

The  typography  of  this  work  is  altogether  in  good  taste. 


From  the  Cincinnati  Gazette. 

Mrs.  Willard’s  School  History  of  the  United  States.— It  is  one  of  those 
rare  things,  a good  schuol-book  ; infinitely  better  than  any  of  the  United  States 
Histones  fitted  for  schools,  which  we  have  at  present.  It  is  quite  full  enough, 
and  yet  condensed  with  great  care  and  skill.  The  style  is  clear  and  simple — 
Mrs.  Willard  having  avoided  those  immense  Johnsonian  words  w hich  Gnmshaw 
and  other  writers  for  children  love  to  put  into  their  works,  while,  at  the  same 
time  there  is  nothing  of  the  pap  style  about  it.  The  arrangement  is  exoellen' 

(20) 


Willard’s  Series  of  Sc  ho  >/  Histories  and  Charts. 


the  chapters  of  a good  length  ; every  page  is  dated,  and  a marginal  index  makes 
reference  easy.  But  the  best  feature  in  the  work  is  its  series  of  maps  ; we  have 
the  country  as  it  was  when  filled  with  Indians ; as  granted  to  Gilbert . as  di- 
vided at  the  time  the  Pilgrims  came  over;  as  apportioned  in  1643;  the  West 
w hile  in  possession  of  France  ; the  Atlantic  coast  in  1T33  ; in  1763 ; as  in  the 
Revolution,  with  the  position  of  the  army  at  various  points  ; at  the  close  of  the 
Revolutionary  War ; during  the  war  of  1812-15 ; and  in  1840 : making  eleven 
most  excellent  maps,  such  as  every  school  history  should  have.  When  we 
think  of  the  unintelligible,  incomplete,  badly  written,  badly  arranged,  worthless 
work  of  Grimshaw  which  has  been  .so  long  used  in  our  schools,  we  feel  that 
every  scholar  and  teacher  owes  a debt  of  gratitude  to  Mrs.  Willard.  Miss 
Robins  has  done  for  English  History,  what  Mrs.  Willard  has  now  done  for 
American,  and  we  trust  these  two  works  will  be  followed  by  others  of  as  high  or 
higher  character.  We  recommend  Mrs.  Willard’s  work  as  better  than  any  we 
know  of  on  the  same  subject ; not  excepting  Bancroft’s  abridgment.  This  work, 
followed  by  the  careful  reading  of  Mr  Bancroft’s  full  work,  is  all  that  would  be 
needed  up  to  the  point  where  Bancroft  stops ; from  that  point,  Pitkin  and  Mar- 
shall imperfectly  supply  the  place,  which  Bancroft  and  Sparks  will  soon  fUL 


From  the  United  States  Gazette. 

Mrs.  Willard  is  well  known  throughout  the  country  as  a lady  of  high  attain 
ments,  who  has  distinguished  herself  as  the  Principal  of  Female  Academies,  that 
have  sent  abroad  some  of  the  most  accomplished  females  of  the  land. 

The  plan  of  the  authoress  is  to  divide  the  time  into  periods,  of  which  the  be- 
ginning and  the  end  are  marked  by  some  important  event,  and  then  care  has 
been  taken  to  make  plain  the  events  of  intermediate  periods.  The  style  is  clear, 
and  there  appears  no  confusion  in  the  narrative.  In  looking  through  the  work, 
we  do  not  discover  that  the  author  has  any  early  prejudices  to  gratify.  The 
book,  therefore,  so  far  as  we  have  been  able  to  judge,  may  be  safely  recom- 
mended as  one  of  great  merit,  and  the  maps  and  marginal  notes,  and  series  of 
questions,  give  additional  value  to  the  work. 


From  the  Vr  u-buryport  Watchman. 

An  Abridged  History  of  the  United  States  : By  Emma  Willard. — We 
think  we  are  warranted  in  saying,  that  it  is  better  adapted  to  meet  the  wants  of 
our  schools  and  academies  in  which  history  is  pursued,  than  any  other  work  of 
the  kind  now  before  the  public. 

The  style  is  perspicuous  and  flowing,  and  the  prominent  points  of  our  history  are 
presented  in  such  a manner  as  to  make  a deep  and  lasting  impression  on  the  mind. 

We  could  conscientiously  say  much  more  in  praise  of  this  book,  but  inust  content 
ourselves  by  heartily  commending  it  to  the  attention  of  those  who  are  anxious 
to  find  a good  text-book  of  American  history  for  the  use  of  schools. 

From  the  Albany  Evening  Journal . 

Wu  lard’s  United  States. — This  work  is  well  printed  on  strong  white  paper, 
and  is  bound  in  a plain  substantial  manner — all-important  requisites  in  a school- 
book. The  text  is  prepared  with  equal  skill  and  judgment.  The  memory  of  the 
youthful  student  is  aided  by  a number  of  spirited  illustrations — by  no  means  un- 
important auxiliaries — while  to  lighten  the  labors  of  the  teacher,  a series  of  ques- 
tions is  adapted  to  each  chapter.  Nor  is  its  usefulness  limited  to  the  school-room 
As  a book  of  reference  for  editors,  lawyers,  politicians,  and  others,  where  dates  and 
facts  connected  with  every  important  event  in  American  History  may  be  readily 
found,  this  little  book  is  truly  valuable- 


91 


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